1
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Liu W, Niu Z, Cheng W, Li X, Duan CK, Yin Z, Rong X, Du J. Experimental Test of the Jarzynski Equality in a Single Spin-1 System Using High-Fidelity Single-Shot Readouts. PHYSICAL REVIEW LETTERS 2023; 131:220401. [PMID: 38101345 DOI: 10.1103/physrevlett.131.220401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Revised: 10/22/2023] [Accepted: 10/24/2023] [Indexed: 12/17/2023]
Abstract
The Jarzynski equality (JE), which connects the equilibrium free energy with nonequilibrium work statistics, plays a crucial role in quantum thermodynamics. Although practical quantum systems are usually multilevel systems, most tests of the JE were executed in two-level systems. A rigorous test of the JE by directly measuring the work distribution of a physical process in a high-dimensional quantum system remains elusive. Here, we report an experimental test of the JE in a single spin-1 system. We realized nondemolition projective measurement of this three-level system via cascading high-fidelity single-shot readouts and directly measured the work distribution utilizing the two-point measurement protocol. The validity of the JE was verified from the nonadiabatic to adiabatic zone and under different effective temperatures. Our work puts the JE on a solid experimental foundation and makes the nitrogen-vacancy (NV) center system a mature toolbox to perform advanced experiments of stochastic quantum thermodynamics.
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Affiliation(s)
- Wenquan Liu
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China
| | - Zhibo Niu
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Wei Cheng
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xin Li
- Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Chang-Kui Duan
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Zhangqi Yin
- Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Xing Rong
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jiangfeng Du
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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2
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Koshihara K, Yuasa K. Quantum ergotropy and quantum feedback control. Phys Rev E 2023; 107:064109. [PMID: 37464633 DOI: 10.1103/physreve.107.064109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2023] [Accepted: 05/08/2023] [Indexed: 07/20/2023]
Abstract
We study the energy extraction from and charging to a finite-dimensional quantum system by general quantum operations. We prove that the changes in energy induced by unital quantum operations are limited by the ergotropy and charging bounds for unitary quantum operations. This implies that, in order to break the ergotropy bound for unitary quantum operations, one needs to perform a quantum operation with feedback control. We also show that the ergotropy bound for unital quantum operations, applied to initial thermal equilibrium states, is tighter than the inequality representing the standard second law of thermodynamics without feedback control.
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Affiliation(s)
- Kenta Koshihara
- Department of Physics, Waseda University, Tokyo 169-8555, Japan
| | - Kazuya Yuasa
- Department of Physics, Waseda University, Tokyo 169-8555, Japan
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3
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Henao I, Uzdin R. Catalytic Leverage of Correlations and Mitigation of Dissipation in Information Erasure. PHYSICAL REVIEW LETTERS 2023; 130:020403. [PMID: 36706391 DOI: 10.1103/physrevlett.130.020403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2022] [Revised: 09/12/2022] [Accepted: 12/13/2022] [Indexed: 06/18/2023]
Abstract
Correlations are a valuable resource for quantum information processing and quantum thermodynamics. However, the preparation of some correlated states can carry a substantial cost that should be compared against its value. We show that classical correlations generated in information erasure can be catalytically exploited, which enables us to mitigate the resulting dissipation of heat and entropy. Because these correlations are a byproduct of erasure, they can be considered free. Our framework consists of a composition of two transformations, where an initial erasure transformation is followed by a catalytic mitigation of dissipation. Although we also show that maximum erasure with minimum dissipation and no correlations is theoretically possible, catalysts are always useful in practical erasure settings, where correlations are expected to take place.
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Affiliation(s)
- I Henao
- Fritz Haber Research Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - R Uzdin
- Fritz Haber Research Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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4
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Jiang Y, Chen T, Xiao C, Pan K, Jin G, Yu Y, Chen A. Quantum Battery Based on Hybrid Field Charging. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1821. [PMID: 36554226 PMCID: PMC9777628 DOI: 10.3390/e24121821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Revised: 12/07/2022] [Accepted: 12/12/2022] [Indexed: 06/17/2023]
Abstract
A quantum battery consisting of an ensemble two-level atom is investigated. The battery is charged simultaneously by a harmonic field and an electrostatic field. The results show that the hybrid charging is superior to the previous case of only harmonic field charging in terms of battery capacity and charging power, regardless of whether the interaction between atoms is considered or not. In addition, the repulsive interaction between atoms will increase the battery capacity and charging power, while the attractive interaction between atoms will reduce the battery capacity and discharge power.
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5
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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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6
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He GG, Zhang FL. Preparation of quantum correlations assisted by a steering Maxwell demon. Phys Rev E 2022; 106:014119. [PMID: 35974593 DOI: 10.1103/physreve.106.014119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Accepted: 07/01/2022] [Indexed: 06/15/2023]
Abstract
A Maxwell demon can reduce the entropy of a quantum system by performing measurements on its environment. The nonsignaling theorem prevents the demon from affecting the average state of the system. We study the preparations of quantum correlations from a system qubit and an auxiliary qubit, assisted by a demon who obtains information of the system qubit from measurements on its environment. The demon can affect the postmeasured states of system by choosing different measurements, which establishes the relationships between quantum steering and other correlations in the thermodynamic framework. We present the optimal protocols for creating mutual information, entanglement, and Bell-nonlocality. These maximal correlations are found to relate exactly to the steerable boundary of the system-environment state with maximally mixed marginals. We also present upper bounds of the prepared correlations by utilizing classical environment-system correlation, which can be regarded as steering-type inequalities bounding the correlations created with the aid of classical demons.
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Affiliation(s)
- Gang-Gang He
- Department of Physics, School of Science, Tianjin University, Tianjin 300072, China
| | - Fu-Lin Zhang
- Department of Physics, School of Science, Tianjin University, Tianjin 300072, China
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7
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Salazar DSP. Upper bound for quantum entropy production from entropy flux. Phys Rev E 2022; 105:L042101. [PMID: 35590526 DOI: 10.1103/physreve.105.l042101] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2021] [Accepted: 03/08/2022] [Indexed: 06/15/2023]
Abstract
Entropy production is a key quantity characterizing nonequilibrium systems. However, it can often be difficult to compute in practice, as it requires detailed information about the system and the dynamics it undergoes. This becomes even more difficult in the quantum domain and if one is interested in generic nonequilibrium reservoirs, for which the standard thermal recipes no longer apply. In this paper, we derive an upper bound for the entropy production in terms of the entropy flux for a class of systems for which the flux is given in terms of a system's observable. Since currents are often easily accessible in this class of systems, this bound should prove useful for estimating the entropy production in a broad variety of processes. We illustrate the applicability of the bound by considering a three-level maser engine and a system interacting with a squeezed bath.
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Affiliation(s)
- Domingos S P Salazar
- Unidade de Educação a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco, Brazil
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8
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Ji W, Chai Z, Wang M, Guo Y, Rong X, Shi F, Ren C, Wang Y, Du J. Spin Quantum Heat Engine Quantified by Quantum Steering. PHYSICAL REVIEW LETTERS 2022; 128:090602. [PMID: 35302812 DOI: 10.1103/physrevlett.128.090602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 01/25/2022] [Indexed: 06/14/2023]
Abstract
Following the rising interest in quantum information science, the extension of a heat engine to the quantum regime by exploring microscopic quantum systems has seen a boon of interest in the last decade. Although quantum coherence in the quantum system of the working medium has been investigated to play a nontrivial role, a complete understanding of the intrinsic quantum advantage of quantum heat engines remains elusive. We experimentally demonstrate that the quantum correlation between the working medium and the thermal bath is critical for the quantum advantage of a quantum Szilárd engine, where quantum coherence in the working medium is naturally excluded. By quantifying the nonclassical correlation through quantum steering, we reveal that the heat engine is quantum when the demon can truly steer the working medium. The average work obtained by taking different ways of work extraction on the working medium can be used to verify the real quantum Szilárd engine.
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Affiliation(s)
- Wentao Ji
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Zihua Chai
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Mengqi Wang
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Yuhang Guo
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xing Rong
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Fazhan Shi
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Changliang Ren
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| | - Ya Wang
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Jiangfeng Du
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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9
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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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10
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Touil A, Weber K, Deffner S. Quantum Euler Relation for Local Measurements. ENTROPY (BASEL, SWITZERLAND) 2021; 23:889. [PMID: 34356429 PMCID: PMC8303509 DOI: 10.3390/e23070889] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Revised: 07/05/2021] [Accepted: 07/08/2021] [Indexed: 01/24/2023]
Abstract
In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to account for the effects of the measurement back action. To this end, we derive a quantum analog of the Euler relation, which is governed by the information retrieved by local quantum measurements. The validity of the relation is demonstrated for the collective dissipation model, where we find that thermodynamic behavior is exhibited in the weak-coupling regime.
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Affiliation(s)
- Akram Touil
- Department of Physics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA; (K.W.); (S.D.)
| | - Kevin Weber
- Department of Physics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA; (K.W.); (S.D.)
- Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA; (K.W.); (S.D.)
- Instituto de Física ‘Gleb Wataghin’, Universidade Estadual de Campinas, Campinas 13083-859, SP, Brazil
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11
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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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12
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Park JJ, Nha H, Kim SW, Vedral V. Information fluctuation theorem for an open quantum bipartite system. Phys Rev E 2020; 101:052128. [PMID: 32575248 DOI: 10.1103/physreve.101.052128] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Accepted: 04/28/2020] [Indexed: 11/07/2022]
Abstract
We study an arbitrary nonequilibrium dynamics of a quantum bipartite system coupled to a reservoir. For its characterization, we present a fluctuation theorem (FT) that explicitly addresses the quantum correlation of subsystems during the thermodynamic evolution. To our aim, we designate the local and the global states altogether in the time-forward and the time-reversed transition probabilities. In view of the two-point measurement scheme, only the global states are subject to measurements whereas the local states are used only as an augmented information on the composite system. We specifically derive a FT in such a form that relates the entropy production of local systems in the time-forward transition to the change of quantum correlation in the time-reversed transition. This also leads to a useful thermodynamic inequality and we illustrate its advantage by an example of an isothermal process on Werner states.
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Affiliation(s)
- Jung Jun Park
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore.,Department of Physics, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar.,Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyunchul Nha
- Department of Physics, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar
| | - Sang Wook Kim
- Department of Physics, Kyung Hee University, Seoul 02447, Republic of Korea
| | - Vlatko Vedral
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore.,Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX13PU, United Kingdom
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13
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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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14
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Diazdelacruz J. Quantum Relative Entropy of Tagging and Thermodynamics. ENTROPY 2020; 22:e22020138. [PMID: 33285913 PMCID: PMC7516547 DOI: 10.3390/e22020138] [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: 11/21/2019] [Revised: 01/10/2020] [Accepted: 01/22/2020] [Indexed: 11/22/2022]
Abstract
Thermodynamics establishes a relation between the work that can be obtained in a transformation of a physical system and its relative entropy with respect to the equilibrium state. It also describes how the bits of an informational reservoir can be traded for work using Heat Engines. Therefore, an indirect relation between the relative entropy and the informational bits is implied. From a different perspective, we define procedures to store information about the state of a physical system into a sequence of tagging qubits. Our labeling operations provide reversible ways of trading the relative entropy gained from the observation of a physical system for adequately initialized qubits, which are used to hold that information. After taking into account all the qubits involved, we reproduce the relations mentioned above between relative entropies of physical systems and the bits of information reservoirs. Some of them hold only under a restricted class of coding bases. The reason for it is that quantum states do not necessarily commute. However, we prove that it is always possible to find a basis (equivalent to the total angular momentum one) for which Thermodynamics and our labeling system yield the same relation.
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Affiliation(s)
- Jose Diazdelacruz
- Department of Applied Physics and Materials Engineering, Universidad Politecnica de Madrid, 28040 Madrid, Spain
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15
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Beyer K, Luoma K, Strunz WT. Steering Heat Engines: A Truly Quantum Maxwell Demon. PHYSICAL REVIEW LETTERS 2019; 123:250606. [PMID: 31922791 DOI: 10.1103/physrevlett.123.250606] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Revised: 07/15/2019] [Indexed: 06/10/2023]
Abstract
We address the question of verifying the quantumness of thermal machines. A Szilárd engine is truly quantum if its work output cannot be described by a local hidden state model, i.e., an objective local statistical ensemble. Quantumness in this scenario is revealed by a steering-type inequality which bounds the classically extractable work. A quantum Maxwell demon can violate that inequality by exploiting quantum correlations between the work medium and the thermal environment. While for a classical Szilárd engine an objective description of the medium always exists, any such description can be ruled out by a steering task in a truly quantum case.
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Affiliation(s)
- Konstantin Beyer
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062, Dresden, Germany
| | - Kimmo Luoma
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062, Dresden, Germany
| | - Walter T Strunz
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062, Dresden, Germany
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16
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Strasberg P. Operational approach to quantum stochastic thermodynamics. Phys Rev E 2019; 100:022127. [PMID: 31574666 DOI: 10.1103/physreve.100.022127] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2018] [Indexed: 06/10/2023]
Abstract
We set up a framework for quantum stochastic thermodynamics based solely on experimentally controllable but otherwise arbitrary interventions at discrete times. Using standard assumptions about the system-bath dynamics and insights from the repeated interaction framework, we define internal energy, heat, work, and entropy at the trajectory level. The validity of the first law (at the trajectory level) and the second law (on average) is established. The theory naturally allows one to treat incomplete information and it is able to smoothly interpolate between a trajectory-based and an ensemble level description. We use our theory to compute the thermodynamic efficiency of recent experiments reporting on the stabilization of photon number states using real-time quantum feedback control. Special attention is paid to limiting cases of our general theory, where we recover or contrast it with previous results. We point out various interesting problems, which the theory is able to address rigorously, such as the detection of quantum effects in thermodynamics.
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Affiliation(s)
- Philipp Strasberg
- Physics and Materials Science Research Unit, University of Luxembourg, 1511 Luxembourg, Luxembourg and Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain
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17
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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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18
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Manzano G, Fazio R, Roldán É. Quantum Martingale Theory and Entropy Production. PHYSICAL REVIEW LETTERS 2019; 122:220602. [PMID: 31283254 DOI: 10.1103/physrevlett.122.220602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2019] [Indexed: 06/09/2023]
Abstract
We employ martingale theory to describe fluctuations of entropy production for open quantum systems in nonequilbrium steady states. Using the formalism of quantum jump trajectories, we identify a decomposition of entropy production into an exponential martingale and a purely quantum term, both obeying integral fluctuation theorems. An important consequence of this approach is the derivation of a set of genuine universal results for stopping-time and infimum statistics of stochastic entropy production. Finally, we complement the general formalism with numerical simulations of a qubit system.
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Affiliation(s)
- Gonzalo Manzano
- International Centre for Theoretical Physics ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
| | - Rosario Fazio
- International Centre for Theoretical Physics ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- NEST, Scuola Normale Superiore and Instituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Édgar Roldán
- International Centre for Theoretical Physics ICTP, Strada Costiera 11, I-34151 Trieste, Italy
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19
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Morris B, Lami L, Adesso G. Assisted Work Distillation. PHYSICAL REVIEW LETTERS 2019; 122:130601. [PMID: 31012629 DOI: 10.1103/physrevlett.122.130601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2018] [Revised: 02/08/2019] [Indexed: 06/09/2023]
Abstract
We study the process of assisted work distillation. This scenario arises when two parties share a bipartite quantum state ρ_{AB} and their task is to locally distill the optimal amount of work when one party is restricted to thermal operations, whereas the other can perform general quantum operations and they are allowed to communicate classically. We demonstrate that this question is intimately related to the distillation of classical and quantum correlations. In particular, we show that the advantage of one party performing global measurements over many copies of ρ_{AB} is related to the nonadditivity of the entanglement of formation. We also show that there may exist work bound in the quantum correlations of the state that is only extractable under the wider class of local Gibbs-preserving operations.
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Affiliation(s)
- Benjamin Morris
- School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Ludovico Lami
- School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Gerardo Adesso
- School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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20
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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: 25] [Impact Index Per Article: 5.0] [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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21
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Andolina GM, Keck M, Mari A, Campisi M, Giovannetti V, Polini M. Extractable Work, the Role of Correlations, and Asymptotic Freedom in Quantum Batteries. PHYSICAL REVIEW LETTERS 2019; 122:047702. [PMID: 30768349 DOI: 10.1103/physrevlett.122.047702] [Citation(s) in RCA: 62] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2018] [Revised: 11/23/2018] [Indexed: 05/28/2023]
Abstract
We investigate a quantum battery made of N two-level systems, which is charged by an optical mode via an energy-conserving interaction. We quantify the fraction of energy stored in the battery that can be extracted in order to perform thermodynamic work. We first demonstrate that this quantity is highly reduced by the presence of correlations between the charger and the battery or between the subsystems composing the battery. We then show that the correlation-induced suppression of extractable energy, however, can be mitigated by preparing the charger in a coherent optical state. We conclude by proving that the charger-battery system is asymptotically free of such locking correlations in the N→∞ limit.
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Affiliation(s)
- Gian Marcello Andolina
- NEST, Scuola Normale Superiore, I-56126 Pisa, Italy
- Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy
| | - Maximilian Keck
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Andrea Mari
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Michele Campisi
- Department of Physics and Astronomy, University of Florence, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
- INFN Sezione di Firenze, via G.Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
| | - Vittorio Giovannetti
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Marco Polini
- Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy
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22
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Quantum Information Remote Carnot Engines and Voltage Transformers. ENTROPY 2019; 21:e21020127. [PMID: 33266843 PMCID: PMC7514606 DOI: 10.3390/e21020127] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/03/2019] [Revised: 01/24/2019] [Accepted: 01/28/2019] [Indexed: 11/17/2022]
Abstract
A physical system out of thermal equilibrium is a resource for obtaining useful work when a heat bath at some temperature is available. Information Heat Engines are the devices which generalize the Szilard cylinders and make use of the celebrated Maxwell demons to this end. In this paper, we consider a thermo-chemical reservoir of electrons which can be exchanged for entropy and work. Qubits are used as messengers between electron reservoirs to implement long-range voltage transformers with neither electrical nor magnetic interactions between the primary and secondary circuits. When they are at different temperatures, the transformers work according to Carnot cycles. A generalization is carried out to consider an electrical network where quantum techniques can furnish additional security.
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