1
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Huang HB, Li G, Dong H. Qubit reset with a shortcut-to-isothermal scheme. Phys Rev E 2024; 109:064132. [PMID: 39020929 DOI: 10.1103/physreve.109.064132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Accepted: 05/16/2024] [Indexed: 07/20/2024]
Abstract
Landauer's principle shows that the minimum energy cost to reset a classical bit in a bath with temperature T is k_{B}Tln2 in the infinite time. However, the task to reset the bit in finite time has posted a new challenge, especially for quantum bit (qubit) where both the operation time and controllability are limited. We design a shortcut-to-isothermal scheme to reset a qubit in finite time τ with limited controllability. The energy cost is minimized with the optimal control scheme with and without bound. This optimal control scheme can provide a reference to realize qubit reset with minimum energy cost for the limited time.
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2
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Huang K, Xi C, Long X, Liu H, Fan YA, Wang X, Zheng Y, Feng Y, Nie X, Lu D. Experimental Realization of Self-Contained Quantum Refrigeration. PHYSICAL REVIEW LETTERS 2024; 132:210403. [PMID: 38856252 DOI: 10.1103/physrevlett.132.210403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Accepted: 04/16/2024] [Indexed: 06/11/2024]
Abstract
A fundamental challenge in quantum thermodynamics is the exploration of inherent dimensional constraints in thermodynamic machines. In the context of two-level systems, the most compact refrigerator necessitates the involvement of three entities, operating under self-contained conditions that preclude the use of external work sources. Here, we build such a smallest refrigerator using a nuclear spin system, where three distinct two-level carbon-13 nuclei in the same molecule are involved to facilitate the refrigeration process. The self-contained feature enables it to operate without relying on net external work, and the unique mechanism sets this refrigerator apart from its classical counterparts. We evaluate its performance under varying conditions and systematically scrutinize the cooling constraints across a spectrum of scenarios, which sheds light on the interplay between quantum information and thermodynamics.
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Affiliation(s)
- Keyi Huang
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Cheng Xi
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China
| | - Xinyue Long
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen 518045, China
| | - Hongfeng Liu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yu-Ang Fan
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiangyu Wang
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yuxuan Zheng
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yufang Feng
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xinfang Nie
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen 518045, China
| | - Dawei Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen 518045, China
- International Quantum Academy, Shenzhen 518055, China
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3
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Xu K, Li HG, Zhu HJ, Liu WM. Inhibiting the self-discharging process of quantum batteries in non-Markovian noises. Phys Rev E 2024; 109:054132. [PMID: 38907473 DOI: 10.1103/physreve.109.054132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Accepted: 05/08/2024] [Indexed: 06/24/2024]
Abstract
One of the main challenges in developing high-performance quantum batteries is the self-discharging process, where energy is dissipated from a quantum battery into the environment. In this work, we investigate the influence of non-Markovian noises on the performance of a quantum battery. Our results demonstrate that adding auxiliary qubits to a quantum battery system can effectively suppress the self-discharging process, leading to an improvement in both the steady-state energy and extractable work. We reveal that the physical mechanism inhibiting the self-discharging process is the formation of system-environment bound states, rather than an increase in non-Markovianity. Our results could be of both theoretical and experimental interest in exploring the ability of quantum batteries to maintain long stored energy in the environment.
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Affiliation(s)
| | | | | | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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4
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Mohammadi A, Shafiee A. Quantum non-Markovianity, quantum coherence and extractable work in a general quantum process. Phys Chem Chem Phys 2024; 26:3990-3999. [PMID: 38224013 DOI: 10.1039/d3cp04528e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2024]
Abstract
A key concept in quantum thermodynamics is extractable work, which specifies the maximum amount of work that can be extracted from a quantum system. Different quantities are used to measure extractable work, the most prevalent of which are ergotropy and the difference between the non-equilibrium and equilibrium quantum free energies. Using the latter, we investigate the evolution of extractable work when an open quantum system undergoes a general quantum process described by a completely-positive and trace-preserving dynamical map. We derive a fundamental equation of thermodynamics for such processes as a relation between the distinct sorts of energy change in such a way that the first and the second law of thermodynamics are combined. We then identify the contributions from the reversible and irreversible processes in this equation and demonstrate that they are respectively responsible for the evolution of heat and extractable work of the open quantum system. Furthermore, we show how this correspondence between irreversibility and extractable work has the potential to provide a clear explanation of how the quantum properties of a system affect its extractable work evolution. Specifically, we establish this by directly connecting the change in extractable work with the change in standard quantifiers of quantum non-Markovianity and quantum coherence during a general quantum process. We illustrate these results with two examples.
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Affiliation(s)
- Amin Mohammadi
- Research Group on Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O. Box 11365-9516, Tehran, Iran.
| | - Afshin Shafiee
- Research Group on Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O. Box 11365-9516, Tehran, Iran.
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5
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Céleri LC, Rudnicki Ł. Gauge-Invariant Quantum Thermodynamics: Consequences for the First Law. ENTROPY (BASEL, SWITZERLAND) 2024; 26:111. [PMID: 38392366 PMCID: PMC10888098 DOI: 10.3390/e26020111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2023] [Revised: 01/22/2024] [Accepted: 01/23/2024] [Indexed: 02/24/2024]
Abstract
The universality of classical thermodynamics rests on the central limit theorem, due to which, measurements of thermal fluctuations are unable to reveal detailed information regarding the microscopic structure of a macroscopic body. When small systems are considered and fluctuations become important, thermodynamic quantities can be understood in the context of classical stochastic mechanics. A fundamental assumption behind thermodynamics is therefore that of coarse graining, which stems from a substantial lack of control over all degrees of freedom. However, when quantum systems are concerned, one claims a high level of control. As a consequence, information theory plays a major role in the identification of thermodynamic functions. Here, drawing from the concept of gauge symmetry-essential in all modern physical theories-we put forward a new possible intermediate route. Working within the realm of quantum thermodynamics, we explicitly construct physically motivated gauge transformations which encode a gentle variant of coarse graining behind thermodynamics. As a first application of this new framework, we reinterpret quantum work and heat, as well as the role of quantum coherence.
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Affiliation(s)
- Lucas C Céleri
- QPequi Group, Institute of Physics, Federal University of Goiás, Goiânia 74690-900, Brazil
| | - Łukasz Rudnicki
- International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland
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6
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Vom Ende F, Malvetti E. The Thermomajorization Polytope and Its Degeneracies. ENTROPY (BASEL, SWITZERLAND) 2024; 26:106. [PMID: 38392361 PMCID: PMC10888266 DOI: 10.3390/e26020106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Revised: 01/19/2024] [Accepted: 01/22/2024] [Indexed: 02/24/2024]
Abstract
Drawing inspiration from transportation theory, in this work, we introduce the notions of "well-structured" and "stable" Gibbs states and we investigate their implications for quantum thermodynamics and its resource theory approach via thermal operations. It is found that, in the quasi-classical realm, global cyclic state transfers are impossible if and only if the Gibbs state is stable. Moreover, using a geometric approach by studying the so-called thermomajorization polytope, we prove that any subspace in equilibrium can be brought out of equilibrium via thermal operations. Interestingly, the case of some subsystem being in equilibrium can be witnessed via the degenerate extreme points of the thermomajorization polytope, assuming that the Gibbs state of the system is well structured. These physical considerations are complemented by simple new constructions for the polytope's extreme points, as well as for an important class of extremal Gibbs-stochastic matrices.
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Affiliation(s)
- Frederik Vom Ende
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - Emanuel Malvetti
- School of Natural Sciences, Technische Universität München, 85737 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST) & Munich Quantum Valley (MQV), 80799 München, Germany
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7
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Purktimatanont K, Mohdee V, Pancharoen U, Maneeintr K, Punyain W, Lothongkum AW. Synergistic effect of arsenic removal from petroleum condensate via liquid-liquid extraction: Thermodynamics, kinetics, DFT and McCabe-Thiele method. Heliyon 2023; 9:e23143. [PMID: 38205073 PMCID: PMC10777394 DOI: 10.1016/j.heliyon.2023.e23143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2023] [Revised: 11/08/2023] [Accepted: 11/27/2023] [Indexed: 01/12/2024] Open
Abstract
This work presents the purification of petroleum condensate by removing arsenic ions via liquid-liquid extraction (LLE). Influence of pure and synergistic extractants is investigated. In terms of the practicability, following parameters are examined: the type of extractant, operating time, and temperature. Response surface methodology is used to design parameters such as organic-aqueous ratio and extractant concentration. Under optimal conditions; a mixture of 1 mol/L HCl and 0.02 mol/L thiourea with an organic/aqueous ratio of 1:4 at 323.15 K for 60 min, the extraction of arsenic reached 78.2 %. Further, batch simulation via two-stage counter-current extraction, and estimation by McCabe-Thiele diagram proved to be enhanced arsenic extraction to 95.3 %. Analysis by FTIR show that arsenic ions in petroleum condensate are formed as triphenylarsine compound ((C6H5)3As). The process of arsenic removal proved to be zero-order endothermic, irreversible and spontaneous reaction. The results obtained from the density functional theory (DFT) confirm that arsenic ions react with the synergistic extractant: effectively forming a covalent bond (As-S).
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Affiliation(s)
- Kittamuk Purktimatanont
- Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, 10330, Thailand
| | - Vanee Mohdee
- Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, 10330, Thailand
| | - Ura Pancharoen
- Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, 10330, Thailand
| | - Kreangkrai Maneeintr
- Carbon Capture, Storage and Utilization Research Group, Department of Mining and, Petroleum Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, 10330, Thailand
| | - Wikorn Punyain
- Department of Chemistry and Center of Excellence in Biomaterials, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand
| | - Anchaleeporn W. Lothongkum
- Department of Chemical Engineering, School of Engineering, King Mongkut's Institute of Technology Ladkrabang, Ladkrabang, Bangkok, 10520, Thailand
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8
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Datta C, Varun Kondra T, Miller M, Streltsov A. Catalysis of entanglement and other quantum resources. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:116002. [PMID: 37733010 DOI: 10.1088/1361-6633/acfbec] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Accepted: 09/21/2023] [Indexed: 09/22/2023]
Abstract
In chemistry, a catalyst is a substance which enables a chemical reaction or increases its rate, while remaining unchanged in the process. Instead of chemical reactions,quantum catalysisenhances our ability to convert quantum states into each other under physical constraints. The nature of the constraints depends on the problem under study and can arise, e.g. from energy preservation. This article reviews the most recent developments in quantum catalysis and gives a historical overview of this research direction. We focus on the catalysis of quantum entanglement and coherence, and also discuss this phenomenon in quantum thermodynamics and general quantum resource theories. We review applications of quantum catalysis and also discuss the recent efforts on universal catalysis, where the quantum state of the catalyst does not depend on the states to be transformed. Catalytic embezzling is also considered, a phenomenon that occurs if the catalyst's state can change in the transition.
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Affiliation(s)
- Chandan Datta
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
- Institute for Theoretical Physics III, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Tulja Varun Kondra
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Marek Miller
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Alexander Streltsov
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
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9
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Cerisola F, Mayo F, Roncaglia AJ. A Wigner Quasiprobability Distribution of Work. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1439. [PMID: 37895560 PMCID: PMC10606729 DOI: 10.3390/e25101439] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Revised: 10/06/2023] [Accepted: 10/08/2023] [Indexed: 10/29/2023]
Abstract
In this article, we introduce a quasiprobability distribution of work that is based on the Wigner function. This proposal rests on the idea that the work conducted on an isolated system can be coherently measured by coupling the system to a quantum measurement apparatus. In this way, a quasiprobability distribution of work can be defined in terms of the Wigner function of the apparatus. This quasidistribution contains the information of the work statistics and also holds a clear operational definition that can be directly measured in a real experiment. Moreover, it is shown that the presence of quantum coherence in the energy eigenbasis is related with the appearance of features related to non-classicality in the Wigner function such as negativity and interference fringes. On the other hand, from this quasiprobability distribution, it is straightforward to obtain the standard two-point measurement probability distribution of work and also the difference in average energy for initial states with coherences.
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Affiliation(s)
- Federico Cerisola
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EGA, Argentina; (F.M.); (A.J.R.)
- Instituto de Física de Buenos Aires (IFIBA), CONICET—Universidad de Buenos Aires, Buenos Aires C1121A6B, Argentina
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
- Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
| | - Franco Mayo
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EGA, Argentina; (F.M.); (A.J.R.)
- Instituto de Física de Buenos Aires (IFIBA), CONICET—Universidad de Buenos Aires, Buenos Aires C1121A6B, Argentina
| | - Augusto J. Roncaglia
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EGA, Argentina; (F.M.); (A.J.R.)
- Instituto de Física de Buenos Aires (IFIBA), CONICET—Universidad de Buenos Aires, Buenos Aires C1121A6B, Argentina
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10
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Kolchinsky A. Generalized Zurek's bound on the cost of an individual classical or quantum computation. Phys Rev E 2023; 108:034101. [PMID: 37849139 DOI: 10.1103/physreve.108.034101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 06/13/2023] [Indexed: 10/19/2023]
Abstract
We consider the minimal thermodynamic cost of an individual computation, where a single input x is mapped to a single output y. In prior work, Zurek proposed that this cost was given by K(x|y), the conditional Kolmogorov complexity of x given y (up to an additive constant that does not depend on x or y). However, this result was derived from an informal argument, applied only to deterministic computations, and had an arbitrary dependence on the choice of protocol (via the additive constant). Here we use stochastic thermodynamics to derive a generalized version of Zurek's bound from a rigorous Hamiltonian formulation. Our bound applies to all quantum and classical processes, whether noisy or deterministic, and it explicitly captures the dependence on the protocol. We show that K(x|y) is a minimal cost of mapping x to y that must be paid using some combination of heat, noise, and protocol complexity, implying a trade-off between these three resources. Our result is a kind of "algorithmic fluctuation theorem" with implications for the relationship between the second law and the Physical Church-Turing thesis.
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Affiliation(s)
- Artemy Kolchinsky
- Universal Biology Institute, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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11
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Akhouri U, Shandera S, Yesmurzayeva G. Increasing Extractable Work in Small Qubit Landscapes. ENTROPY (BASEL, SWITZERLAND) 2023; 25:947. [PMID: 37372291 DOI: 10.3390/e25060947] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Revised: 05/25/2023] [Accepted: 06/06/2023] [Indexed: 06/29/2023]
Abstract
An interesting class of physical systems, including those associated with life, demonstrates the ability to hold thermalization at bay and perpetuate states of high free-energy compared to a local environment. In this work we study quantum systems with no external sources or sinks for energy, heat, work, or entropy that allow for high free-energy subsystems to form and persist. We initialize systems of qubits in mixed, uncorrelated states and evolve them subject to a conservation law. We find that four qubits make up the minimal system for which these restricted dynamics and initial conditions allow an increase in extractable work for a subsystem. On landscapes of eight co-evolving qubits, interacting in randomly selected subsystems at each step, we demonstrate that restricted connectivity and an inhomogeneous distribution of initial temperatures both lead to landscapes with longer intervals of increasing extractable work for individual qubits. We demonstrate the role of correlations that develop on the landscape in enabling a positive change in extractable work.
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Affiliation(s)
- Unnati Akhouri
- Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
| | - Sarah Shandera
- Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
| | - Gaukhar Yesmurzayeva
- Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
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12
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The nonequilibrium cost of accurate information processing. Nat Commun 2022; 13:7155. [DOI: 10.1038/s41467-022-34541-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2022] [Accepted: 10/28/2022] [Indexed: 11/24/2022] Open
Abstract
AbstractAccurate information processing is crucial both in technology and in nature. To achieve it, any information processing system needs an initial supply of resources away from thermal equilibrium. Here we establish a fundamental limit on the accuracy achievable with a given amount of nonequilibrium resources. The limit applies to arbitrary information processing tasks and arbitrary information processing systems subject to the laws of quantum mechanics. It is easily computable and is expressed in terms of an entropic quantity, which we name the reverse entropy, associated to a time reversal of the information processing task under consideration. The limit is achievable for all deterministic classical computations and for all their quantum extensions. As an application, we establish the optimal tradeoff between nonequilibrium and accuracy for the fundamental tasks of storing, transmitting, cloning, and erasing information. Our results set a target for the design of new devices approaching the ultimate efficiency limit, and provide a framework for demonstrating thermodynamical advantages of quantum devices over their classical counterparts.
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13
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Shi HL, Ding S, Wan QK, Wang XH, Yang WL. Entanglement, Coherence, and Extractable Work in Quantum Batteries. PHYSICAL REVIEW LETTERS 2022; 129:130602. [PMID: 36206414 DOI: 10.1103/physrevlett.129.130602] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 08/22/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
We investigate the connection between quantum resources and extractable work in quantum batteries. We demonstrate that quantum coherence in the battery or the battery-charger entanglement is a necessary resource for generating nonzero extractable work during the charging process. At the end of the charging process, we also establish a tight link of coherence and entanglement with the final extractable work: coherence naturally promotes the coherent work while coherence and entanglement inhibit the incoherent work. We also show that obtaining maximally coherent work is faster than obtaining maximally incoherent work. Examples ranging from the central-spin battery and the Tavis-Cummings battery to the spin-chain battery are given to illustrate these results.
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Affiliation(s)
- Hai-Long Shi
- School of Physics, Northwest University, Xi'an 710127, China
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, APM, Chinese Academy of Sciences, Wuhan 430071, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Shu Ding
- School of Physics, Northwest University, Xi'an 710127, China
| | - Qing-Kun Wan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, APM, Chinese Academy of Sciences, Wuhan 430071, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xiao-Hui Wang
- School of Physics, Northwest University, Xi'an 710127, China
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
- Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China
| | - Wen-Li Yang
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
- Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China
- Institute of Modern Physics, Northwest University, Xi'an 710127, China
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14
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Puliyil S, Banik M, Alimuddin M. Thermodynamic Signatures of Genuinely Multipartite Entanglement. PHYSICAL REVIEW LETTERS 2022; 129:070601. [PMID: 36018679 DOI: 10.1103/physrevlett.129.070601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 07/19/2022] [Indexed: 06/15/2023]
Abstract
The theory of bipartite entanglement shares profound similarities with thermodynamics. In this Letter we extend this connection to multipartite quantum systems where entanglement appears in different forms with genuine entanglement being the most exotic one. We propose thermodynamic quantities that capture a signature of genuineness in multipartite entangled states. Instead of entropy, these quantities are defined in terms of energy-particularly the difference between global and local extractable works (ergotropies) that can be stored in quantum batteries. Some of these quantities suffice as faithful measures of genuineness and to some extent distinguish different classes of genuinely entangled states. Along with scrutinizing properties of these measures we compare them with the other existing genuine measures, and argue that they can serve the purpose in a better sense. Furthermore, the generality of our approach allows us to define suitable functions of ergotropies capturing the signature of k nonseparability that characterizes qualitatively different manifestations of entanglement in multipartite systems.
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Affiliation(s)
- Samgeeth Puliyil
- School of Physics, IISER Thiruvananthapuram, Vithura, Kerala 695551, India
| | - Manik Banik
- Department of Theoretical Sciences, S.N. Bose National Center for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
| | - Mir Alimuddin
- School of Physics, IISER Thiruvananthapuram, Vithura, Kerala 695551, India
- Department of Theoretical Sciences, S.N. Bose National Center for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
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15
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Ptaszyński K. Non-Markovian thermal operations boosting the performance of quantum heat engines. Phys Rev E 2022; 106:014114. [PMID: 35974499 DOI: 10.1103/physreve.106.014114] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 06/21/2022] [Indexed: 06/15/2023]
Abstract
It is investigated whether non-Markovianity, i.e., the memory effects resulting from the coupling of the system to its environment, can be beneficial for the performance of quantum heat engines. Specifically, two physical models are considered. The first one is a well-known single-qubit Otto engine; the non-Markovian behavior is there implemented by replacing standard thermalization strokes with so-called extremal thermal operations which cannot be realized without the memory effects. The second one is a three-stroke engine in which the cycle consists of two extremal thermal operations and a single qubit rotation. It is shown that the non-Markovian Otto engine can generate more work-per-cycle for a given efficiency than its Markovian counterpart, whereas performance of both setups is superior to the three-stroke engine. Furthermore, both the non-Markovian Otto engine and the three-stroke engine can reduce the work fluctuations in comparison with the Markovian Otto engine, with their relative advantage depending on the performance target. This demonstrates the beneficial influence of non-Markovianity on both the average performance and the stability of operation of quantum heat engines.
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Affiliation(s)
- Krzysztof Ptaszyński
- Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland
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16
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Biswas T, Junior ADO, Horodecki M, Korzekwa K. Fluctuation-dissipation relations for thermodynamic distillation processes. Phys Rev E 2022; 105:054127. [PMID: 35706282 DOI: 10.1103/physreve.105.054127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2021] [Accepted: 04/13/2022] [Indexed: 06/15/2023]
Abstract
The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, we first characterize optimal thermodynamic distillation processes, and then we prove a relation between the amount of free energy dissipated in such processes and the free-energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or an arbitrary number of independent energy-incoherent systems, and they allow not only for a state transformation but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure, and thermodynamically free communication, up to second-order asymptotics in the number N of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite N.
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Affiliation(s)
- Tanmoy Biswas
- International Centre for Theory of Quantum Technologies, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - A de Oliveira Junior
- Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland
| | - Michał Horodecki
- International Centre for Theory of Quantum Technologies, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Kamil Korzekwa
- Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland
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17
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Smith A, Sinha K, Jarzynski C. Quantum Coherences and Classical Inhomogeneities as Equivalent Thermodynamics Resources. ENTROPY 2022; 24:e24040474. [PMID: 35455137 PMCID: PMC9029084 DOI: 10.3390/e24040474] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Revised: 03/23/2022] [Accepted: 03/24/2022] [Indexed: 02/05/2023]
Abstract
Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution of a system’s initial state. We compare the amount of work that can be obtained from quantum coherences with the amount that can be obtained from classical inhomogeneities, and find them to be equal in the semiclassical limit. We thus conclude that coherences do not provide a unique thermodynamic advantage of quantum systems over classical systems, in situations where a well-defined semiclassical correspondence exists.
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Affiliation(s)
- Andrew Smith
- Department of Physics, University of Maryland, College Park, MD 20742, USA;
| | - Kanupriya Sinha
- Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA;
- School of Electrical, Computer and Energy Engineering, Arizona State University, Phoenix, AZ 85287, USA
| | - Christopher Jarzynski
- Department of Physics, University of Maryland, College Park, MD 20742, USA;
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
- Correspondence:
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18
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Zakavati S, Tabesh FT, Salimi S. Bounds on charging power of open quantum batteries. Phys Rev E 2021; 104:054117. [PMID: 34942849 DOI: 10.1103/physreve.104.054117] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Accepted: 10/19/2021] [Indexed: 11/07/2022]
Abstract
In general, quantum systems most likely undergo open-system dynamics due to their smallness and sensitivity. Energy storage devices, so-called quantum batteries, are not excluded from this phenomenon. Here, we study fundamental bounds on the power of open quantum batteries from the geometric point of view. By defining an activity operator, a tight upper bound on the charging power is derived for the open quantum batteries in terms of the fluctuations of the activity operator and the quantum Fisher information. The variance of the activity operator may be interpreted as a generalized thermodynamic force, while the quantum Fisher information describes the speed of evolution in the state space of the battery. The thermodynamic interpretation of the upper bound is discussed in detail. As an example, a model for the battery, taking into account the environmental effects, is proposed, and the effect of dissipation and decoherence during the charging process on both the stored work and the charging power is investigated. Our results show that the upper bound is saturated in some time intervals. Also, the maximum value of both the stored work and the corresponding power is achieved in the non-Markovian underdamped regime.
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Affiliation(s)
- Shadab Zakavati
- Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Iran
| | - Fatemeh T Tabesh
- Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Iran
| | - Shahriar Salimi
- Department of Physics, University of Kurdistan, P.O. Box 66177-15175, Sanandaj, Iran
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19
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Heat Modulation on Target Thermal Bath via Coherent Auxiliary Bath. ENTROPY 2021; 23:e23091183. [PMID: 34573807 PMCID: PMC8464766 DOI: 10.3390/e23091183] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Revised: 08/22/2021] [Accepted: 09/05/2021] [Indexed: 12/22/2022]
Abstract
We study a scheme of thermal management where a three-qubit system assisted with a coherent auxiliary bath (CAB) is employed to implement heat management on a target thermal bath (TTB). We consider the CAB/TTB being ensemble of coherent/thermal two-level atoms (TLAs), and within the framework of collision model investigate the characteristics of steady heat current (also called target heat current (THC)) between the system and the TTB. It demonstrates that with the help of the quantum coherence of ancillae the magnitude and direction of heat current can be controlled only by adjusting the coupling strength of system-CAB. Meanwhile, we also show that the influences of quantum coherence of ancillae on the heat current strongly depend on the coupling strength of system—CAB, and the THC becomes positively/negatively correlated with the coherence magnitude of ancillae when the coupling strength below/over some critical value. Besides, the system with the CAB could serve as a multifunctional device integrating the thermal functions of heat amplifier, suppressor, switcher and refrigerator, while with thermal auxiliary bath it can only work as a thermal suppressor. Our work provides a new perspective for the design of multifunctional thermal device utilizing the resource of quantum coherence from the CAB.
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20
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Seah S, Perarnau-Llobet M, Haack G, Brunner N, Nimmrichter S. Quantum Speed-Up in Collisional Battery Charging. PHYSICAL REVIEW LETTERS 2021; 127:100601. [PMID: 34533344 DOI: 10.1103/physrevlett.127.100601] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Revised: 07/01/2021] [Accepted: 08/06/2021] [Indexed: 06/13/2023]
Abstract
We present a collision model for the charging of a quantum battery by identical nonequilibrium qubit units. When the units are prepared in a mixture of energy eigenstates, the energy gain in the battery can be described by a classical random walk, where both average energy and variance grow linearly with time. Conversely, when the qubits contain quantum coherence, interference effects buildup in the battery and lead to a faster spreading of the energy distribution, reminiscent of a quantum random walk. This can be exploited for faster and more efficient charging of a battery initialized in the ground state. Specifically, we show that coherent protocols can yield higher charging power than any possible incoherent strategy, demonstrating a quantum speed-up at the level of a single battery. Finally, we characterize the amount of extractable work from the battery through the notion of ergotropy.
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Affiliation(s)
- Stella Seah
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | | | - Géraldine Haack
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | - Nicolas Brunner
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | - Stefan Nimmrichter
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Siegen 57068, Germany
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21
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Purves T, Short AJ. Channels, measurements, and postselection in quantum thermodynamics. Phys Rev E 2021; 104:014111. [PMID: 34412318 DOI: 10.1103/physreve.104.014111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Accepted: 06/17/2021] [Indexed: 11/07/2022]
Abstract
We analyze the benefit, in terms of extracting work, of having a single use of a quantum channel or measurement in quantum thermodynamics. This highlights a connection between unital and catalytic channels, and some subtleties concerning the conditional work cost of implementing a measurement given that a certain result was obtained. We also consider postselected measurements and show that any nontrivial postselection leads to an unbounded work benefit.
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Affiliation(s)
- Tom Purves
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Anthony J Short
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
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22
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Currencies in Resource Theories. ENTROPY 2021; 23:e23060755. [PMID: 34204010 PMCID: PMC8233888 DOI: 10.3390/e23060755] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Revised: 06/09/2021] [Accepted: 06/11/2021] [Indexed: 11/24/2022]
Abstract
How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like perfectly independent copies of states or exact knowledge of a quantum state. Here we introduce the general tool of “currencies” to quantify realistic descriptions of resources, applicable in experimental settings when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out. Currencies are a subset of resources chosen to quantify all the other resources—like Bell pairs in LOCC or a lifted weight in thermodynamics. We show that from very weak assumptions in the theory we can already find useful currencies that give us necessary and sufficient conditions for resource conversion, and we build up more results as we impose further structure. This work generalizes axiomatic approaches to thermodynamic entropy, work and currencies made of local copies. In particular, by applying our approach to the resource theory of unital maps, we derive operational single-shot entropies for arbitrary, non-probabilistic descriptions of resources.
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23
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Vallejo A, Romanelli A, Donangelo R. Qubit thermodynamics far from equilibrium: Two perspectives about the nature of heat and work in the quantum regime. Phys Rev E 2021; 103:042105. [PMID: 34005920 DOI: 10.1103/physreve.103.042105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2020] [Accepted: 03/15/2021] [Indexed: 11/07/2022]
Abstract
Considering an entropy-based division of energy transferred into heat and work, we develop an alternative theoretical framework for the thermodynamic analysis of two-level systems. When comparing these results with those obtained using the standard definitions of these quantities, we observe the appearance of a different term of work, which represents the energy cost of rotating the Bloch vector in the presence of the external field that defines the local Hamiltonian. Additionally, we obtain explicit expressions for the temperature, the heat capacity, and the internal entropy production of the system in both paradigms. In order to illustrate our findings we study, from both perspectives, matter-radiation interaction processes for two different systems.
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Affiliation(s)
- Andrés Vallejo
- Facultad de Ingeniería, Universidad de la República, 11300 Montevideo, Uruguay
| | - Alejandro Romanelli
- Facultad de Ingeniería, Universidad de la República, 11300 Montevideo, Uruguay
| | - Raúl Donangelo
- Facultad de Ingeniería, Universidad de la República, 11300 Montevideo, Uruguay
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24
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Shiraishi N, Sagawa T. Quantum Thermodynamics of Correlated-Catalytic State Conversion at Small Scale. PHYSICAL REVIEW LETTERS 2021; 126:150502. [PMID: 33929260 DOI: 10.1103/physrevlett.126.150502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Revised: 02/02/2021] [Accepted: 03/18/2021] [Indexed: 06/12/2023]
Abstract
The class of possible thermodynamic conversions can be extended by introducing an auxiliary system called catalyst, which assists in state conversion while its own state remains unchanged. We reveal a complete characterization of catalytic state conversion in quantum and single-shot thermodynamics by allowing an infinitesimal correlation between the system and the catalyst. Specifically, we prove that a single thermodynamic potential, which provides the necessary and sufficient condition for the correlated-catalytic state conversion, is given by the standard nonequilibrium free energy defined with the Kullback-Leibler divergence. This resolves the conjecture raised by Wilming, Gallego, and Eisert [Entropy 19, 241 (2017)ENTRFG1099-430010.3390/e19060241] and by Lostaglio and Müller [Phys. Rev. Lett. 123, 020403 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.020403] in the positive. Moreover, we show that, with the aid of the work storage, any quantum state can be converted into another by paying the work cost equal to the nonequilibrium free energy difference. Our result would serve as a step towards establishing resource theories of catalytic state conversion in the fully quantum regime.
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Affiliation(s)
- Naoto Shiraishi
- Department of Physics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan
| | - Takahiro Sagawa
- Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), The University of Tokyo, 7-3-1 Hongo, Byunkyo-ku, Tokyo 113-8656, Japan
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25
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Bound on Efficiency of Heat Engine from Uncertainty Relation Viewpoint. ENTROPY 2021; 23:e23040439. [PMID: 33918678 PMCID: PMC8068911 DOI: 10.3390/e23040439] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Revised: 03/21/2021] [Accepted: 03/22/2021] [Indexed: 11/16/2022]
Abstract
Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. For example, a heat engine can be modeled with an infinite potential well as the working substance to determine the efficiency and work done. However, in this method, the relationship between the quantum observables and the physically measurable parameters-i.e., the efficiency and work done-is not well understood from the quantum mechanics approach. A detailed analysis is needed to link the thermodynamic variables (on which the efficiency and work done depends) with the uncertainty principle for better understanding. Here, we present the connection of the sum uncertainty relation of position and momentum operators with thermodynamic variables in the quantum heat engine model. We are able to determine the upper and lower bounds on the efficiency of the heat engine through the uncertainty relation.
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26
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Łobejko M. The tight Second Law inequality for coherent quantum systems and finite-size heat baths. Nat Commun 2021; 12:918. [PMID: 33568672 PMCID: PMC7876128 DOI: 10.1038/s41467-021-21140-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 01/13/2021] [Indexed: 11/08/2022] Open
Abstract
In classical thermodynamics, the optimal work is given by the free energy difference, what according to the result of Skrzypczyk et al. can be generalized for individual quantum systems. The saturation of this bound, however, requires an infinite bath and ideal energy storage that is able to extract work from coherences. Here we present the tight Second Law inequality, defined in terms of the ergotropy (rather than free energy), that incorporates both of those important microscopic effects - the locked energy in coherences and the locked energy due to the finite-size bath. The former is solely quantified by the so-called control-marginal state, whereas the latter is given by the free energy difference between the global passive state and the equilibrium state. Furthermore, we discuss the thermodynamic limit where the finite-size bath correction vanishes, and the locked energy in coherences takes the form of the entropy difference. We supplement our results by numerical simulations for the heat bath given by the collection of qubits and the Gaussian model of the work reservoir.
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Affiliation(s)
- Marcin Łobejko
- Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308, Gdańsk, Poland.
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27
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Singh V, Müstecaplıoğlu ÖE. Performance bounds of nonadiabatic quantum harmonic Otto engine and refrigerator under a squeezed thermal reservoir. Phys Rev E 2021; 102:062123. [PMID: 33466082 DOI: 10.1103/physreve.102.062123] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 11/16/2020] [Indexed: 11/07/2022]
Abstract
We analyze the performance of a quantum Otto cycle, employing a time-dependent harmonic oscillator as the working fluid undergoing sudden expansion and compression strokes during the adiabatic stages, coupled to a squeezed reservoir. First, we show that the maximum efficiency that our engine can achieve is 1/2 only, which is in contrast with earlier studies claiming unit efficiency under the effect of a squeezed reservoir. Then, in the high-temperature limit, we obtain analytic expressions for the upper bound on the efficiency as well as on the coefficient of performance of the Otto cycle. The obtained bounds are independent of the parameters of the system and depend on the reservoir parameters only. Additionally, with a hot squeezed thermal bath, we obtain an analytic expression for the efficiency at maximum work which satisfies the derived upper bound. Further, in the presence of squeezing in the cold reservoir, we specify an operational regime for the Otto refrigerator otherwise forbidden in the standard case. Finally, we find the cost of creating a squeezed state from the thermal state and show that in order to harvest the benefits of squeezing, it is sufficient to squeeze only one mode of the reservoir in resonance with the transition frequency of the working fluid. Further, we show that when the cost of squeezing is included in the definition of the operational efficiency of the engine, the advantages of squeezing fade away. Still, being purely quantum mechanical fuel in nature, squeezed reservoirs are beneficial in their own way by providing us with more compact energy storage medium or offering effectively high-temperature baths without being actually too hot.
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Affiliation(s)
- Varinder Singh
- Department of Physics, Koç University, 34450 Sarıyer, Istanbul, Turkey
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28
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Bernardo BDL. Unraveling the role of coherence in the first law of quantum thermodynamics. Phys Rev E 2020; 102:062152. [PMID: 33466045 DOI: 10.1103/physreve.102.062152] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Accepted: 12/11/2020] [Indexed: 11/07/2022]
Abstract
One of the fundamental questions in the emerging field of quantum thermodynamics is the role played by coherence in energetic processes that occur at the quantum level. Here we address this issue by investigating two different quantum versions of the first law of thermodynamics, derived from the classical definitions of work and heat. By doing so, we find out that there exists a mathematical inconsistency between both scenarios. We further show that the energetic contribution of the dynamics of coherence is the key ingredient to establish the consistency. Some examples involving two-level atomic systems are discussed in order to illustrate our findings.
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Affiliation(s)
- Bertúlio de Lima Bernardo
- Departamento de Física, Universidade Federal da Paraíba, 58051-900 João Pessoa, PB, Brazil.,Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande-PB, Brazil
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29
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Gong H, Wang Y, Zhang HD, Xu RX, Zheng X, Yan Y. Thermodynamic free-energy spectrum theory for open quantum systems. J Chem Phys 2020; 153:214115. [DOI: 10.1063/5.0028429] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Hong Gong
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hou-Dao Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM) and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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30
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Francica G, Binder FC, Guarnieri G, Mitchison MT, Goold J, Plastina F. Quantum Coherence and Ergotropy. PHYSICAL REVIEW LETTERS 2020; 125:180603. [PMID: 33196219 DOI: 10.1103/physrevlett.125.180603] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2020] [Revised: 08/13/2020] [Accepted: 09/22/2020] [Indexed: 06/11/2023]
Abstract
Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the instantaneous energy eigenbasis of the dynamical system. Thermodynamic cycles can, in principle, be designed to extract work from this nonequilibrium resource. Here, we isolate and study the quantum coherent component to the work yield in such protocols. Specifically, we identify a coherent contribution to the ergotropy (the maximum amount of unitarily extractable work via cyclical variation of Hamiltonian parameters). We show this by dividing the optimal transformation into an incoherent operation and a coherence extraction cycle. We obtain bounds for both the coherent and incoherent parts of the extractable work and discuss their saturation in specific settings. Our results are illustrated with several examples, including finite-dimensional systems and bosonic Gaussian states that describe recent experiments on quantum heat engines with a quantized load.
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Affiliation(s)
- G Francica
- CNR-SPIN, I-84084 Fisciano (Salerno), Italy
| | - F C Binder
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - G Guarnieri
- School of Physics, Trinity College Dublin, Dublin 2, Ireland
| | - M T Mitchison
- School of Physics, Trinity College Dublin, Dublin 2, Ireland
| | - J Goold
- School of Physics, Trinity College Dublin, Dublin 2, Ireland
| | - F Plastina
- Dipartimento di Fisica, Università della Calabria, 87036 Arcavacata di Rende (CS), Italy
- INFN-Gruppo Collegato di Cosenza
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31
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Alimuddin M, Guha T, Parashar P. Independence of work and entropy for equal-energetic finite quantum systems: Passive-state energy as an entanglement quantifier. Phys Rev E 2020; 102:012145. [PMID: 32795079 DOI: 10.1103/physreve.102.012145] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2020] [Accepted: 07/07/2020] [Indexed: 11/07/2022]
Abstract
Although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic (EE) states in the asymptotic limit, for the finite quantum systems, the relation is not so linear and requires detailed investigation. Toward this, we have considered a resource theoretic framework taking the energy preserving operations (EPOs) as free, to compare the amount of extractable work from two different quantum states. Under the EPO, majorization becomes a necessary criterion for state transformation. It is also shown that the passive-state energy is a concave function, and, for EE states, it becomes proportional to the ergotropy in absolute sense. Invariance of the passive-state energy under unitary action on the given state makes it an entanglement measure for the pure bipartite states. Furthermore, due to the nonadditivity of passive-state energy for the different system Hamiltonians, one can generate Vidal^{'}s monotones which would give the optimal probability for pure entangled state transformation. This measure also quantifies the ergotropic gap which is employed to distinguish some specific classes of three-qubit pure entangled states.
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Affiliation(s)
- Mir Alimuddin
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B T Road, Kolkata-700108, India
| | - Tamal Guha
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B T Road, Kolkata-700108, India
| | - Preeti Parashar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B T Road, Kolkata-700108, India
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32
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García-Pintos LP, Hamma A, Del Campo A. Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries. PHYSICAL REVIEW LETTERS 2020; 125:040601. [PMID: 32794781 DOI: 10.1103/physrevlett.125.040601] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
We study the connection between the charging power of quantum batteries and the fluctuations of the extractable work. We prove that in order to have a nonzero rate of change of the extractable work, the state ρ_{W} of the battery cannot be an eigenstate of a "free energy operator," defined by F≡H_{W}+β^{-1}log(ρ_{W}), where H_{W} is the Hamiltonian of the battery and β is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the free energy operator upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine.
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Affiliation(s)
- Luis Pedro García-Pintos
- Joint Center for Quantum Information and Computer Science and Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - Alioscia Hamma
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - Adolfo Del Campo
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
- Donostia International Physics Center, E-20018 San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
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33
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Dolatkhah H, Salimi S, Khorashad AS, Haseli S. The entropy production for thermal operations. Sci Rep 2020; 10:9757. [PMID: 32546716 PMCID: PMC7298041 DOI: 10.1038/s41598-020-66416-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Accepted: 05/14/2020] [Indexed: 11/28/2022] Open
Abstract
According to the first and second laws of thermodynamics and the definitions of work and heat, microscopic expressions for the non-equilibrium entropy production have been achieved. Recently, a redefinition of heat has been presented in [Nature Communications volume 8, Article number: 2180 (2017)]. Since thermal operations play an important role in the resource theory of thermodynamics, it would be very interesting to find out the effect of the above-mentioned definition on the expression of the entropy production for these kind of operations. This is one of the aims of the present paper. Using the new definition of heat, it is shown that the entropy production is the same as the mutual information between a system and a bath both for thermal operations and, if the system-bath initial state is factorized, for entropy-preserving operations. It is also discussed that how one can recognize the type of the correlation between a system and a bath through knowledge of the initial state of the system only. It is shown that if the initial state of a system is diagonal in the energy basis, the thermal operations cannot create a quantum correlation between the system and the bath, however, if the system initial state is coherent Gibbs state, there cannot be classical correlation due to the thermal operations.
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Affiliation(s)
- H Dolatkhah
- Department of Physics, University of Kurdistan, P. O. Box: 66177-15175, Sanandaj, Iran
| | - S Salimi
- Department of Physics, University of Kurdistan, P. O. Box: 66177-15175, Sanandaj, Iran
| | - A S Khorashad
- Department of Physics, University of Kurdistan, P. O. Box: 66177-15175, Sanandaj, Iran.
| | - S Haseli
- Faculty of Physics, Urmia University of Technology, Urmia, Iran
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34
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Can Thermodynamic Behavior of Alice's Particle Affect Bob's Particle? Sci Rep 2020; 10:9045. [PMID: 32493988 PMCID: PMC7270105 DOI: 10.1038/s41598-020-65800-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2020] [Accepted: 05/04/2020] [Indexed: 11/09/2022] Open
Abstract
We propose an experiment to investigate the possibility of long-distance thermodynamic relationships between two entangled particles. We consider a pair of spin-\documentclass[12pt]{minimal}
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\begin{document}$$\frac{1}{2}$$\end{document}12 particles prepared in an entangled singlet state in which one particle is sent to Alice and the other to her distant mate Bob, who are spatially separated. Our proposed experiment consists of three different setups: First, both particles are coupled to two heat baths with various temperatures. In the second setup, only Alice’s particle is coupled to a heat bath and finally, in the last setup, only Bob’s particle is coupled to a heat bath. We study the evolution of an open quantum system using the first law of thermodynamics based on the concepts of ergotropy, adiabatic work, and operational heat, in a quantum fashion. We analyze and compare ergotropy and heat transfer in three setups. Our results show that the heat transfer for each entangled particle is not independent of the thermalization process that occurs for the other one. We prove that the existence of quantum correlations affects the thermodynamic behavior of distant particles in an entangled state.
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35
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Vallejo A, Romanelli A, Donangelo R. Out-of-equilibrium quantum thermodynamics in the Bloch sphere: Temperature and internal entropy production. Phys Rev E 2020; 101:042132. [PMID: 32422716 DOI: 10.1103/physreve.101.042132] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2019] [Accepted: 04/08/2020] [Indexed: 11/07/2022]
Abstract
An explicit expression for the temperature of an open two-level quantum system is obtained as a function of local properties under the hypothesis of weak interaction with the environment. This temperature is defined for both equilibrium and out-of-equilibrium states and coincides with the environment temperature if the system reaches thermal equilibrium with a heat reservoir. Additionally, we show that within this theoretical framework the total entropy production can be partitioned into two contributions: one due to heat transfer and another, associated to internal irreversibilities, related to the loss of internal coherence by the qubit. The positiveness of the heat capacity is established, as well as its consistency with the well-known results at thermal equilibrium. We apply these concepts to two different systems and show that they behave in analogous ways as their classical counterparts.
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Affiliation(s)
- Andrés Vallejo
- Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay
| | | | - Raúl Donangelo
- Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay
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36
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Beretta GP. The fourth law of thermodynamics: steepest entropy ascent. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190168. [PMID: 32223406 DOI: 10.1098/rsta.2019.0168] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/18/2019] [Indexed: 05/18/2023]
Abstract
When thermodynamics is understood as the science (or art) of constructing effective models of natural phenomena by choosing a minimal level of description capable of capturing the essential features of the physical reality of interest, the scientific community has identified a set of general rules that the model must incorporate if it aspires to be consistent with the body of known experimental evidence. Some of these rules are believed to be so general that we think of them as laws of Nature, such as the great conservation principles, whose 'greatness' derives from their generality, as masterfully explained by Feynman in one of his legendary lectures. The second law of thermodynamics is universally contemplated among the great laws of Nature. In this paper, we show that in the past four decades, an enormous body of scientific research devoted to modelling the essential features of non-equilibrium natural phenomena has converged from many different directions and frameworks towards the general recognition (albeit still expressed in different but equivalent forms and language) that another rule is also indispensable and reveals another great law of Nature that we propose to call the 'fourth law of thermodynamics'. We state it as follows: every non-equilibrium state of a system or local subsystem for which entropy is well defined must be equipped with a metric in state space with respect to which the irreversible component of its time evolution is in the direction of steepest entropy ascent compatible with the conservation constraints. To illustrate the power of the fourth law, we derive (nonlinear) extensions of Onsager reciprocity and fluctuation-dissipation relations to the far-non-equilibrium realm within the framework of the rate-controlled constrained-equilibrium approximation (also known as the quasi-equilibrium approximation). This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.
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37
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Newman D, Mintert F, Nazir A. Quantum limit to nonequilibrium heat-engine performance imposed by strong system-reservoir coupling. Phys Rev E 2020; 101:052129. [PMID: 32575334 DOI: 10.1103/physreve.101.052129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Accepted: 04/17/2020] [Indexed: 06/11/2023]
Abstract
We show that finite system-reservoir coupling imposes a distinct quantum limit on the performance of a nonequilibrium quantum heat engine. Even in the absence of quantum friction along the isentropic strokes, finite system-reservoir coupling induces correlations that result in the generation of coherence between the energy eigenstates of the working system. This coherence acts to hamper the engine's power output, as well as the efficiency with which it can convert heat into useful work, and cannot be captured by a standard Born-Markov analysis of the system-reservoir interactions.
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Affiliation(s)
- David Newman
- Department of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
- Department of Physics, Imperial College London, London, SW7 2AZ, United Kingdom
| | - Florian Mintert
- Department of Physics, Imperial College London, London, SW7 2AZ, United Kingdom
| | - Ahsan Nazir
- Department of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
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38
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Measurement Induced Synthesis of Coherent Quantum Batteries. Sci Rep 2019; 9:19628. [PMID: 31873161 PMCID: PMC6928017 DOI: 10.1038/s41598-019-56158-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Accepted: 12/02/2019] [Indexed: 11/17/2022] Open
Abstract
Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.
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39
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Faist P, Sagawa T, Kato K, Nagaoka H, Brandão FGSL. Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2019; 123:250601. [PMID: 31922799 DOI: 10.1103/physrevlett.123.250601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2019] [Indexed: 06/10/2023]
Abstract
The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same thermodynamic potential. As an intermediate result, we show for a general state that if the gap between the min- and the max-relative entropies to the thermal state is small, then the state can be approximately reversibly converted to and from the thermal state with thermal operations and a small source of coherence. Our proof provides a quantum version of the Shannon-McMillan-Breiman theorem for the relative entropy and a quantum Stein's lemma for ergodic states and local Gibbs states. Our results provide a strong link between the abstract resource theory of thermodynamics and more realistic physical systems as we achieve a robust and operational characterization of the emergence of a thermodynamic potential in translation-invariant lattice systems.
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Affiliation(s)
- Philippe Faist
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Institute for Theoretical Physics, ETH Zurich 8093, Switzerland
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - Takahiro Sagawa
- Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
| | - Kohtaro Kato
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Hiroshi Nagaoka
- The University of Electro-Communications, Tokyo 182-8585, Japan
| | - Fernando G S L Brandão
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Google Inc., Venice, California 90291, USA
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40
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Clivaz F, Silva R, Haack G, Brask JB, Brunner N, Huber M. Unifying paradigms of quantum refrigeration: Fundamental limits of cooling and associated work costs. Phys Rev E 2019; 100:042130. [PMID: 31770926 DOI: 10.1103/physreve.100.042130] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Indexed: 11/07/2022]
Abstract
In classical thermodynamics the work cost of control can typically be neglected. On the contrary, in quantum thermodynamics the cost of control constitutes a fundamental contribution to the total work cost. Here, focusing on quantum refrigeration, we investigate how the level of control determines the fundamental limits to cooling and how much work is expended in the corresponding process. We compare two extremal levels of control: first, coherent operations, where the entropy of the resource is left unchanged, and, second, incoherent operations, where only energy at maximum entropy (i.e., heat) is extracted from the resource. For minimal machines, we find that the lowest achievable temperature and associated work cost depend strongly on the type of control, in both single-cycle and asymptotic regimes. We also extend our analysis to general machines. Our work provides a unified picture of the different approaches to quantum refrigeration developed in the literature, including algorithmic cooling, autonomous quantum refrigerators, and the resource theory of quantum thermodynamics.
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Affiliation(s)
- Fabien Clivaz
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland.,Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
| | - Ralph Silva
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
| | - Géraldine Haack
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
| | - Jonatan Bohr Brask
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland.,Department of Physics, Technical University of Denmark, Fysikvej, Kongens Lyngby 2800, Denmark
| | - Nicolas Brunner
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
| | - Marcus Huber
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
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41
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Mendes LRS, Soares-Pinto DO. Time as a consequence of internal coherence. Proc Math Phys Eng Sci 2019; 475:20190470. [PMID: 31824220 DOI: 10.1098/rspa.2019.0470] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2019] [Accepted: 10/10/2019] [Indexed: 11/12/2022] Open
Abstract
Time has been an elusive concept to grasp. Although we do not yet understand it properly, there have been advances made in regard to how we can explain it. One such advance is the Page-Wootters mechanism. In this mechanism, time is seen as an inaccessible coordinate and the apparent passage of time arises as a consequence of correlations between the subsystems of a global state. Here we propose a measure that captures the relational character of the mechanism, showing that the internal coherence is the necessary ingredient for the emergence of time in the Page-Wootters model. Also, we connect it to results in quantum thermodynamics, showing that it is directly related to the extractable work from quantum coherence.
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Affiliation(s)
- Leandro R S Mendes
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970, São Carlos, São Paulo, Brazil
| | - Diogo O Soares-Pinto
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970, São Carlos, São Paulo, Brazil
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42
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Lostaglio M. An introductory review of the resource theory approach to thermodynamics. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:114001. [PMID: 31546240 DOI: 10.1088/1361-6633/ab46e5] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics covered include the so-called 'many second laws of thermodynamics', thermo-majorisation and symmetry constraints on the evolution of quantum coherence. Among the elementary applications, I explicitly work out the bounds on deterministic work extraction and formation, discuss the complete solution of the theory for a single qubit and present the irreversibility of coherence transfers. The aim is to facilitate the task of those researchers interested in engaging and contributing to this topic, presenting scope and motivation of its core assumptions and discussing the relation between the resource theory and complementary approaches.
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Affiliation(s)
- Matteo Lostaglio
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), 08860, Spain
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43
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Mohammady MH, Romito A. Efficiency of a cyclic quantum heat engine with finite-size baths. Phys Rev E 2019; 100:012122. [PMID: 31499920 DOI: 10.1103/physreve.100.012122] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Indexed: 11/07/2022]
Abstract
In this paper we investigate the relationship between the efficiency of a cyclic quantum heat engine with the Hilbert space dimension of the thermal baths. By means of a general inequality, we show that the Carnot efficiency can be obtained only when both the hot and cold baths are infinitely large. By further introducing a specific model where the baths are constituted of ensembles of finite-dimensional particles, we further demonstrate the relationship between the engine's power and efficiency, with the dimension of the working substance and the bath particles.
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Affiliation(s)
- M Hamed Mohammady
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom.,RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava 84511, Slovakia
| | - Alessandro Romito
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom
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44
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Piccione N, Militello B, Napoli A, Bellomo B. Simple scheme for extracting work with a single bath. Phys Rev E 2019; 100:032143. [PMID: 31639978 DOI: 10.1103/physreve.100.032143] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2019] [Indexed: 11/07/2022]
Abstract
We propose a simple protocol exploiting the thermalization of a storage bipartite system S to extract work from a resource system R. The protocol is based on a recent work definition involving only a single bath. A general description of the protocol is provided without specifying the characteristics of S. We quantify both the extracted work and the ideal efficiency of the process, also giving maximum bounds for them. Then, we apply the protocol to two cases: two interacting qubits and the Rabi model. In both cases, for very strong couplings, an extraction of work comparable with the bare energies of the subsystems of S is obtained and its peak is reached for finite values of the bath temperature, T. We finally show, in the Rabi model at T=0, how to transfer the work stored in S to an external device, permitting thus a cyclic implementation of the whole work-extraction protocol. Our proposal makes use of simple operations not needing fine control.
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Affiliation(s)
- Nicolò Piccione
- Institut UTINAM, CNRS UMR 6213, Université Bourgogne Franche-Comté, Observatoire des Sciences de l'Univers THETA, 41 bis avenue de l'Observatoire, F-25010 Besançon, France
| | - Benedetto Militello
- Università degli Studi di Palermo, Dipartimento di Fisica e Chimica - Emilio Segrè, via Archirafi 36, I-90123 Palermo, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Catania, via Santa Sofia 64, I-95123 Catania, Italy
| | - Anna Napoli
- Università degli Studi di Palermo, Dipartimento di Fisica e Chimica - Emilio Segrè, via Archirafi 36, I-90123 Palermo, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Catania, via Santa Sofia 64, I-95123 Catania, Italy
| | - Bruno Bellomo
- Institut UTINAM, CNRS UMR 6213, Université Bourgogne Franche-Comté, Observatoire des Sciences de l'Univers THETA, 41 bis avenue de l'Observatoire, F-25010 Besançon, France
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45
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Guha T, Alimuddin M, Parashar P. Allowed and forbidden bipartite correlations from thermal states. Phys Rev E 2019; 100:012147. [PMID: 31499776 DOI: 10.1103/physreve.100.012147] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2019] [Indexed: 11/07/2022]
Abstract
The strong connection between correlations and quantum thermodynamics raises a natural question about the preparation of correlated quantum states from two copies of a thermal qubit. In this work we study the specific forms of allowed and forbidden bipartite correlations. As a consequence, we extend the result to separable but not absolutely separable class of product states. Preparation of a general form of entanglement from arbitrary thermal qubits is studied and, as an application, we propose a strategy to establish desired entanglement between two distant parties. The threshold temperature to produce entanglement from two copies of a thermal qubit has also been discussed from the resource theoretic perspective, which ensures that the bound on the temperature can be superseded with the help of a resource state. A dimension dependent upper bound on the temperature is derived, below which two copies of any d-dimensional thermal state can be entangled in 2×d dimensions.
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Affiliation(s)
- Tamal Guha
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
| | - Mir Alimuddin
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
| | - Preeti Parashar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
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46
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Abstract
The presence of correlations in physical systems can be a valuable resource for many quantum information tasks. They are also relevant in thermodynamic transformations, and their creation is usually associated to some energetic cost. In this work, we study the role of correlations in the thermodynamic process of state formation in the single-shot regime, and find that correlations can also be viewed as a resource. First, we show that the energetic cost of creating multiple copies of a given state can be reduced by allowing correlations in the final state. We obtain the minimum cost for every finite number of subsystems, and then we show that this feature is not restricted to the case of copies. More generally, we demonstrate that in the asymptotic limit, by allowing a logarithmic amount of correlations, we can recover standard results where the free energy quantifies this minimum cost. Correlations in quantum thermodynamics are usually regarded as a useful but expensive resource. Here, the authors prove that the work cost of generating multiple copies of a state is lower if the copies are correlated, pointing out at the irreversibility of the process in the single-shot regime.
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47
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Guarnieri G, Ng NHY, Modi K, Eisert J, Paternostro M, Goold J. Quantum work statistics and resource theories: Bridging the gap through Rényi divergences. Phys Rev E 2019; 99:050101. [PMID: 31212510 DOI: 10.1103/physreve.99.050101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2018] [Indexed: 06/09/2023]
Abstract
The work performed on or extracted from a nonautonomous quantum system described by means of a two-point projective-measurement approach is a stochastic variable. We show that the cumulant generating function of work can be recast in the form of quantum Rényi-α divergences, and by exploiting the convexity of this cumulant generating function, derive a single-parameter family of bounds for the first moment of work. Higher order moments of work can also be obtained from this result. In this way, we establish a link between quantum work statistics in stochastic approaches and resource theories for quantum thermodynamics, a theory in which Rényi-α divergences take a central role. To explore this connection further, we consider an extended framework involving a control switch and an auxiliary battery, which is instrumental to reconstructing the work statistics of the system. We compare and discuss our bounds on the work distribution to findings on deterministic work studied in resource-theoretic settings.
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Affiliation(s)
- G Guarnieri
- School of Physics, Trinity College Dublin, Dublin 2, Ireland
| | - N H Y Ng
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - K Modi
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - M Paternostro
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - J Goold
- School of Physics, Trinity College Dublin, Dublin 2, Ireland
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48
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Francica G, Goold J, Plastina F. Role of coherence in the nonequilibrium thermodynamics of quantum systems. Phys Rev E 2019; 99:042105. [PMID: 31108617 DOI: 10.1103/physreve.99.042105] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Indexed: 06/09/2023]
Abstract
Exploiting the relative entropy of coherence, we isolate the coherent contribution in the energetics of a driven nonequilibrium quantum system. We prove that a division of the irreversible work can be made into a coherent and incoherent part. This provides an operational criterion for quantifying the coherent contribution in a generic nonequilibrium transformation on a closed quantum system. We then study such a contribution in two physical models of a driven qubit and kicked rotor. In addition, we also show that coherence generation is connected to the nonadiabaticity of a processes, for which it gives the dominant contribution for slow-enough transformations. The amount of generated coherence in the energy eigenbasis is equivalent to the change in diagonal entropy, and here we show that it fulfills a fluctuation theorem.
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Affiliation(s)
- G Francica
- Dip. Fisica, Università della Calabria, 87036 Arcavacata di Rende (CS), Italy
- INFN-Gruppo Collegato di Cosenza, 87036, Cosenza, Italy
| | - J Goold
- School of Physics, Trinity College Dublin, Dublin 2, D02 PN40, Ireland
| | - F Plastina
- Dip. Fisica, Università della Calabria, 87036 Arcavacata di Rende (CS), Italy
- INFN-Gruppo Collegato di Cosenza, 87036, Cosenza, Italy
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49
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Manzano G, Silva R, Parrondo JMR. Autonomous thermal machine for amplification and control of energetic coherence. Phys Rev E 2019; 99:042135. [PMID: 31108722 DOI: 10.1103/physreve.99.042135] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2017] [Indexed: 06/09/2023]
Abstract
We present a model for an autonomous quantum thermal machine composed of two qubits capable of manipulating and even amplifying the local coherence in a nondegenerate external system. The machine uses only thermal resources, namely, contact with two heat baths at different temperatures, and the external system has a nonzero initial amount of coherence. The method we propose allows for an interconversion between energy, both work and heat, and coherence in an autonomous configuration working in out-of-equilibrium conditions. This model raises interesting questions about the role of fundamental limitations on transformations involving coherence and opens up new possibilities in the manipulation of coherence by autonomous thermal machines.
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Affiliation(s)
- Gonzalo Manzano
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
- International Center for Theoretical Physics ICTP, Strada Costiera 11, I-34151 Trieste, Italy
| | - Ralph Silva
- Group Département de Physique Appliqueè, Université de Genève, 1211 Genève, Switzerland
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Juan M R Parrondo
- Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense Madrid, 28040 Madrid, Spain
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50
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Korzekwa K, Chubb CT, Tomamichel M. Avoiding Irreversibility: Engineering Resonant Conversions of Quantum Resources. PHYSICAL REVIEW LETTERS 2019; 122:110403. [PMID: 30951333 DOI: 10.1103/physrevlett.122.110403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2018] [Revised: 02/10/2019] [Indexed: 06/09/2023]
Abstract
We identify and explore the intriguing property of resource resonance arising within resource theories of entanglement, coherence, and thermodynamics. While the theories considered are reversible asymptotically, the same is generally not true in realistic scenarios where the available resources are bounded. The finite-size effects responsible for this irreversibility could potentially prohibit small quantum information processors or thermal machines from achieving their full potential. Nevertheless, we show here that by carefully engineering the resource interconversion process any such losses can be greatly suppressed. Our results are predicted by higher order expansions of the trade-off between the rate of resource interconversion and the achieved fidelity, and are verified by exact numerical optimizations of the appropriate underlying approximate majorization conditions.
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Affiliation(s)
- Kamil Korzekwa
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia
| | - Christopher T Chubb
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia
| | - Marco Tomamichel
- Centre for Quantum Software and Information, School of Software, University of Technology Sydney, Sydney, New South Wales 2007, Australia
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