1
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Yin J, Yan Y, Miao M, Tang J, Jiang J, Liu H, Chen Y, Chen Y, Lyu F, Mao Z, He Y, Wan L, Zhou B, Lu J. Diamond with Sp 2-Sp 3 composite phase for thermometry at Millikelvin temperatures. Nat Commun 2024; 15:3871. [PMID: 38719862 PMCID: PMC11079005 DOI: 10.1038/s41467-024-48137-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 04/19/2024] [Indexed: 05/12/2024] Open
Abstract
Temperature is one of the seven fundamental physical quantities. The ability to measure temperatures approaching absolute zero has driven numerous advances in low-temperature physics and quantum physics. Currently, millikelvin temperatures and below are measured through the characterization of a certain thermal state of the system as there is no traditional thermometer capable of measuring temperatures at such low levels. In this study, we develop a kind of diamond with sp2-sp3 composite phase to tackle this problem. The synthesized composite phase diamond (CPD) exhibits a negative temperature coefficient, providing an excellent fit across a broad temperature range, and reaching a temperature measurement limit of 1 mK. Additionally, the CPD demonstrates low magnetic field sensitivity and excellent thermal stability, and can be fabricated into probes down to 1 micron in diameter, making it a promising candidate for the manufacture of next-generation cryogenic temperature sensors. This development is significant for the low-temperature physics researches, and can help facilitate the transition of quantum computing, quantum simulation, and other related technologies from research to practical applications.
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Affiliation(s)
- Jianan Yin
- CityU-Shenzhen Futian Research Institute, Shenzhen, 518045, China
- Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
| | - Yang Yan
- CityU-Shenzhen Futian Research Institute, Shenzhen, 518045, China
- Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
| | - Mulin Miao
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
- Department of Materials Science and Engineering, City University of Hong Kong, Hong Kong, China
| | - Jiayin Tang
- Department of Physics, City University of Hong Kong, Hong Kong, China
| | - Jiali Jiang
- Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
| | - Hui Liu
- CityU-Shenzhen Futian Research Institute, Shenzhen, 518045, China
- Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
| | - Yuhan Chen
- Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
| | - Yinxian Chen
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
- Department of Materials Science and Engineering, City University of Hong Kong, Hong Kong, China
| | - Fucong Lyu
- CityU-Shenzhen Futian Research Institute, Shenzhen, 518045, China
- Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
| | - Zhengyi Mao
- CityU-Shenzhen Futian Research Institute, Shenzhen, 518045, China
- Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
| | - Yunhu He
- CityU-Shenzhen Futian Research Institute, Shenzhen, 518045, China
- Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
| | - Lei Wan
- CityU-Shenzhen Futian Research Institute, Shenzhen, 518045, China
- Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China
- China Resources Research Institute of Science and Technology Co, Limited, Hong Kong, China
| | - Binbin Zhou
- Shenzhen Institute of Advanced Electronic Materials, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
| | - Jian Lu
- CityU-Shenzhen Futian Research Institute, Shenzhen, 518045, China.
- Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China.
- Hong Kong Branch of National Precious Metals Material Engineering Research Centre, City University of Hong Kong, Hong Kong, China.
- Department of Materials Science and Engineering, City University of Hong Kong, Hong Kong, China.
- Centre for Advanced Structural Materials, City University of Hong Kong Shenzhen Research Institute, Greater Bay Joint Division, Shenyang National Laboratory for Materials Science, Shenzhen, China.
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2
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Mahmood KT, Hasan MA. Experimental demonstration of classical analogous time-dependent superposition of states. Sci Rep 2022; 12:22580. [PMID: 36585446 PMCID: PMC9803682 DOI: 10.1038/s41598-022-27239-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Accepted: 12/28/2022] [Indexed: 12/31/2022] Open
Abstract
One of the quantum theory concepts on which quantum information processing stands is superposition. Here we provide experimental evidence for the existence of classical analogues to the coherent superposition of energy states, which is made possible by the Hertz-type nonlinearity of the granules together with the external driving field. The granules' nonlinear vibrations are projected into the linear modes of vibration, which depend on one another through the phase and form a coherent superposition. We show that the amplitudes of the coherent states form the components of a state vector that spans a two-dimensional Hilbert space, and time enables the system to span its Hilbert space parametrically. Thus, the superposition of states can be exploited in two-state quantum-like computations without decoherence and wave function collapse. Finally, we demonstrate the experimental realization of applying a reversible Hadamard gate to a pure base state that brings the state into a superposition.
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Affiliation(s)
- Kazi T. Mahmood
- grid.254444.70000 0001 1456 7807Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202 USA
| | - M. Arif Hasan
- grid.254444.70000 0001 1456 7807Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202 USA
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3
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Marvian I. Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics. PHYSICAL REVIEW LETTERS 2022; 129:190502. [PMID: 36399730 DOI: 10.1103/physrevlett.129.190502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
In the framework of quantum thermodynamics preparing a quantum system in a general state requires the consumption of two distinct resources, namely, work and energetic coherence. It has been shown that the work cost of preparing a quantum state is determined by its free energy. Considering a similar setting, here we determine the coherence cost of preparing a general state when there are no restrictions on work consumption. More precisely, the coherence cost is defined as the minimum rate of consumption of systems in a pure coherent state, that is needed to prepare copies of the desired system. We show that the coherence cost of any system is determined by its quantum Fisher information about the time parameter, hence introducing a new operational interpretation of this central quantity of quantum metrology. Our resource-theoretic approach also reveals a previously unnoticed connection between two fundamental properties of quantum Fisher information.
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Affiliation(s)
- Iman Marvian
- Departments of Physics and Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA
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4
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Cerisola F, Sapienza F, Roncaglia AJ. Heat engines with single-shot deterministic work extraction. Phys Rev E 2022; 106:034135. [PMID: 36266866 DOI: 10.1103/physreve.106.034135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 08/16/2022] [Indexed: 06/16/2023]
Abstract
We introduce heat engines working in the nanoregime that allow one to extract a finite amount of deterministic work. Using the resource theory approach to themodynamics, we show that the efficiency of these cycles is strictly smaller than Carnot's, and we associate this difference with a fundamental irreversibility that is present in single-shot transformations. When fluctuations in the extracted work are allowed there is a trade-off between their size and the efficiency. As the size of fluctuations increases so does the efficiency and optimal efficiency is attained for unbounded fluctuations, while a certain amount of deterministic work is drawn from the cycle. Finally, we show that when the working medium is composed of many particles, by creating an amount of correlations between the subsystems that scale logarithmically with their number, Carnot's efficiency can also be approached in the asymptotic limit along with deterministic work extraction.
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Affiliation(s)
- Federico Cerisola
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
- Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom
| | - Facundo Sapienza
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina
- Department of Statistics, University of California, Berkeley, 367 Evans Hall, Berkeley, California 94720, USA
| | - Augusto J Roncaglia
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
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5
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Wang P, Guo Z, Cao H. Quantum Incoherence Based Simultaneously on k Bases. ENTROPY 2022; 24:e24050659. [PMID: 35626544 PMCID: PMC9141266 DOI: 10.3390/e24050659] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Revised: 05/06/2022] [Accepted: 05/06/2022] [Indexed: 02/01/2023]
Abstract
Quantum coherence is known as an important resource in many quantum information tasks, which is a basis-dependent property of quantum states. In this paper, we discuss quantum incoherence based simultaneously on k bases using Matrix Theory Method. First, by defining a correlation function m(e,f) of two orthonormal bases e and f, we investigate the relationships between sets I(e) and I(f) of incoherent states with respect to e and f. We prove that I(e)=I(f) if and only if the rank-one projective measurements generated by e and f are identical. We give a necessary and sufficient condition for the intersection I(e)⋂I(f) to include a state except the maximally mixed state. Especially, if two bases e and f are mutually unbiased, then the intersection has only the maximally mixed state. Secondly, we introduce the concepts of strong incoherence and weak coherence of a quantum state with respect to a set B of k bases and propose a measure for the weak coherence. In the two-qubit system, we prove that there exists a maximally coherent state with respect to B when k=2 and it is not the case for k=3.
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6
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Pairwise quantum criteria and teleportation in a spin square complex. Sci Rep 2022; 12:6406. [PMID: 35437310 PMCID: PMC9016083 DOI: 10.1038/s41598-022-10248-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Accepted: 04/05/2022] [Indexed: 11/08/2022] Open
Abstract
Thermal non-classical correlations quantified by concurrence entanglement, local quantum uncertainty, and quantum coherence in a four-qubit square chain are exactly examined. The influences of the Hamiltonian parameters on the mentioned pairwise quantum criteria and fidelity of teleportation are studied, and the most interesting findings are discussed in detail. It is found that the tuning anisotropy results in enhancing the thermal quantum correlations and coherence as well as average fidelity until achieving maximum values. We persuasively deduce that quantum coherence is a more efficient criterion than that of concurrence and local quantum uncertainty to detect the quantumness of a thermal state.
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7
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Ding QM, Fang XX, Lu H. The Tightness of Multipartite Coherence from Spectrum Estimation. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1519. [PMID: 34828217 PMCID: PMC8621860 DOI: 10.3390/e23111519] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Revised: 11/11/2021] [Accepted: 11/13/2021] [Indexed: 01/13/2023]
Abstract
Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is suitable for various coherence measures. Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence. Then, we investigate the tightness of the estimated lower bound of various coherence measures, including the geometric measure of coherence, the l1-norm of coherence, the robustness of coherence, and some convex roof quantifiers of coherence multiqubit GHZ states and linear cluster states. Finally, we demonstrate the spectrum-estimation-based method as well as the other two efficient methods. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation.
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Affiliation(s)
| | | | - He Lu
- School of Physics, Shandong University, Jinan 250100, China; (Q.-M.D.); (X.-X.F.)
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8
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Common Coherence Witnesses and Common Coherent States. ENTROPY 2021; 23:e23091136. [PMID: 34573764 PMCID: PMC8471717 DOI: 10.3390/e23091136] [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: 07/30/2021] [Revised: 08/28/2021] [Accepted: 08/30/2021] [Indexed: 01/26/2023]
Abstract
We show the properties and characterization of coherence witnesses. We show methods for constructing coherence witnesses for an arbitrary coherent state. We investigate the problem of finding common coherence witnesses for certain class of states. We show that finitely many different witnesses W1,W2,⋯,Wn can detect some common coherent states if and only if ∑i=1ntiWi is still a witnesses for any nonnegative numbers ti(i=1,2,⋯,n). We show coherent states play the role of high-level witnesses. Thus, the common state problem is changed into the question of when different high-level witnesses (coherent states) can detect the same coherence witnesses. Moreover, we show a coherent state and its robust state have no common coherence witness and give a general way to construct optimal coherence witnesses for any comparable states.
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9
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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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10
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Marvian I. Coherence distillation machines are impossible in quantum thermodynamics. Nat Commun 2020; 11:25. [PMID: 31911668 PMCID: PMC6946712 DOI: 10.1038/s41467-019-13846-3] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2018] [Accepted: 11/28/2019] [Indexed: 11/24/2022] Open
Abstract
The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence of a coherence distillation machine, i.e., a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate. This is related to another fundamental question: Starting from many copies of noisy quantum clocks which are (approximately) synchronized with a reference clock, can one distill synchronized clocks in pure states, at a non-zero rate? Surprisingly, we find that the answer to both questions is negative for generic (full-rank) mixed states. However, at the same time, it is possible to distill a sub-linear number of pure coherent states with a vanishing error.
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Affiliation(s)
- Iman Marvian
- Departments of Physics & Electrical and Computer Engineering, Duke University, Durham, NC, 27708, USA.
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11
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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: 22] [Impact Index Per Article: 4.4] [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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12
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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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13
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Narasimhachar V, Thompson J, Ma J, Gour G, Gu M. Quantifying Memory Capacity as a Quantum Thermodynamic Resource. PHYSICAL REVIEW LETTERS 2019; 122:060601. [PMID: 30822091 DOI: 10.1103/physrevlett.122.060601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Revised: 09/16/2018] [Indexed: 06/09/2023]
Abstract
The information-carrying capacity of a memory is known to be a thermodynamic resource facilitating the conversion of heat to work. Szilard's engine explicates this connection through a toy example involving an energy-degenerate two-state memory. We devise a formalism to quantify the thermodynamic value of memory in general quantum systems with nontrivial energy landscapes. Calling this the thermal information capacity, we show that it converges to the nonequilibrium Helmholtz free energy in the thermodynamic limit. We compute the capacity exactly for a general two-state (qubit) memory away from the thermodynamic limit, and find it to be distinct from known free energies. We outline an explicit memory-bath coupling that can approximate the optimal qubit thermal information capacity arbitrarily well.
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Affiliation(s)
- Varun Narasimhachar
- Complexity Institute and School of Physical and Mathematical Sciences, Nanyang Technological University, 50 Nanyang Ave, 639798, Singapore
| | - Jayne Thompson
- Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, 117543, Singapore
| | - Jiajun Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084 Beijing, China
| | - Gilad Gour
- Institute for Quantum Science and Technology and Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, T2N 1N4 Alberta, Canada
| | - Mile Gu
- Complexity Institute and School of Physical and Mathematical Sciences, Nanyang Technological University, 50 Nanyang Ave, 639798, Singapore
- Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, 117543, Singapore
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14
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Gour G, Jennings D, Buscemi F, Duan R, Marvian I. Quantum majorization and a complete set of entropic conditions for quantum thermodynamics. Nat Commun 2018; 9:5352. [PMID: 30559428 PMCID: PMC6297236 DOI: 10.1038/s41467-018-06261-7] [Citation(s) in RCA: 57] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2018] [Accepted: 08/20/2018] [Indexed: 11/09/2022] Open
Abstract
What does it mean for one quantum process to be more disordered than another? Interestingly, this apparently abstract question arises naturally in a wide range of areas such as information theory, thermodynamics, quantum reference frames, and the resource theory of asymmetry. Here we use a quantum-mechanical generalization of majorization to develop a framework for answering this question, in terms of single-shot entropies, or equivalently, in terms of semi-definite programs. We also investigate some of the applications of this framework, and remarkably find that, in the context of quantum thermodynamics it provides the first complete set of necessary and sufficient conditions for arbitrary quantum state transformations under thermodynamic processes, which rigorously accounts for quantum-mechanical properties, such as coherence. Our framework of generalized thermal processes extends thermal operations, and is based on natural physical principles, namely, energy conservation, the existence of equilibrium states, and the requirement that quantum coherence be accounted for thermodynamically.
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Affiliation(s)
- Gilad Gour
- Department of Mathematics and Statistics, University of Calgary, Calgary, AB, T2N 1N4, Canada. .,Institute for Quantum Science and Technology, University of Calgary, Calgary, AB, T2N 1N4, Canada.
| | - David Jennings
- Department of Physics, University of Oxford, Oxford, OX1 3PU, UK.,Department of Physics, Imperial College London, London, SW7 2AZ, UK
| | - Francesco Buscemi
- Department of Mathematical Informatics, Nagoya University, Chikusa-ku, Nagoya, 464-8601, Japan
| | - Runyao Duan
- Institute for Quantum Computing, Baidu Inc., 100193, Beijing, China.,Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, 2007, Australia
| | - Iman Marvian
- Departments of Physics & Electrical and Computer Engineering, Duke University, Durham, NC, 27708, USA
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15
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Anshu A, Hsieh MH, Jain R. Quantifying Resources in General Resource Theory with Catalysts. PHYSICAL REVIEW LETTERS 2018; 121:190504. [PMID: 30468589 DOI: 10.1103/physrevlett.121.190504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2017] [Indexed: 06/09/2023]
Abstract
A question that is commonly asked in all areas of physics is how a certain property of a physical system can be used to achieve useful tasks and how to quantify the amount of such a property in a meaningful way. We answer this question by showing that, in a general resource-theoretic framework that allows the use of free states as catalysts, the amount of "resources" contained in a given state, in the asymptotic scenario, is equal to the regularized relative entropy of a resource of that state. While we need to place a few assumptions on our resource-theoretical framework, it is still sufficiently general, and its special cases include quantum resource theories of entanglement, coherence, asymmetry, athermality, nonuniformity, and purity. As a by-product, our result also implies that the amount of noise one has to inject locally to erase all the entanglement contained in an entangled state is equal to the regularized relative entropy of entanglement.
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Affiliation(s)
- Anurag Anshu
- Center for Quantum Technologies, National University of Singapore, 21 Lower Kent Ridge Rd, 119077 Singapore
| | - Min-Hsiu Hsieh
- Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW 2007, Australia
| | - Rahul Jain
- Centre for Quantum Technologies and Department of Computer Science, National University of Singapore and MajuLab CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore
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16
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Ma W, Zhou L, Zhang Q, Li M, Cheng C, Geng J, Rong X, Shi F, Gong J, Du J. Experimental Observation of a Generalized Thouless Pump with a Single Spin. PHYSICAL REVIEW LETTERS 2018; 120:120501. [PMID: 29694055 DOI: 10.1103/physrevlett.120.120501] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Revised: 01/17/2018] [Indexed: 06/08/2023]
Abstract
Adiabatic cyclic modulation of a one-dimensional periodic potential will result in quantized charge transport, which is termed the Thouless pump. In contrast to the original Thouless pump restricted by the topology of the energy band, here we experimentally observe a generalized Thouless pump that can be extensively and continuously controlled. The extraordinary features of the new pump originate from interband coherence in nonequilibrium initial states, and this fact indicates that a quantum superposition of different eigenstates individually undergoing quantum adiabatic following can also be an important ingredient unavailable in classical physics. The quantum simulation of this generalized Thouless pump in a two-band insulator is achieved by applying delicate control fields to a single spin in diamond. The experimental results demonstrate all principal characteristics of the generalized Thouless pump. Because the pumping in our system is most pronounced around a band-touching point, this work also suggests an alternative means to detect quantum or topological phase transitions.
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Affiliation(s)
- Wenchao Ma
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Longwen Zhou
- Department of Physics, National University of Singapore, Singapore 117543, Singapore
| | - Qi Zhang
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Min Li
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Chunyang Cheng
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Jianpei Geng
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xing Rong
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Fazhan Shi
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore 117543, Singapore
| | - Jiangfeng Du
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
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17
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Zhao H, Yu CS. Coherence measure in terms of the Tsallis relative α entropy. Sci Rep 2018; 8:299. [PMID: 29321521 PMCID: PMC5762766 DOI: 10.1038/s41598-017-18692-1] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2017] [Accepted: 12/15/2017] [Indexed: 11/21/2022] Open
Abstract
Coherence is the most fundamental quantum feature of the nonclassical systems. The understanding of coherence within the resource theory has been attracting increasing interest among which the quantification of coherence is an essential ingredient. A satisfactory measure should meet certain standard criteria. It seems that the most crucial criterion should be the strong monotonicity, that is, average coherence doesn’t increase under the (sub-selective) incoherent operations. Recently, the Tsallis relative α entropy has been tried to quantify the coherence. But it was shown to violate the strong monotonicity, even though it can unambiguously distinguish the coherent and the incoherent states with the monotonicity. Here we establish a family of coherence quantifiers which are closely related to the Tsallis relative α entropy. It proves that this family of quantifiers satisfy all the standard criteria and particularly cover several typical coherence measures.
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Affiliation(s)
- Haiqing Zhao
- College of Science, Dalian jiaotong University, Dalian, 116028, China
| | - Chang-Shui Yu
- School of Physics, Dalian University of Technology, Dalian, 116024, China.
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18
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Radhakrishnan C, Parthasarathy M, Jambulingam S, Byrnes T. Quantum coherence of the Heisenberg spin models with Dzyaloshinsky-Moriya interactions. Sci Rep 2017; 7:13865. [PMID: 29066775 PMCID: PMC5655009 DOI: 10.1038/s41598-017-13871-6] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2017] [Accepted: 09/06/2017] [Indexed: 11/23/2022] Open
Abstract
We study quantum coherence in a spin chain with both symmetric exchange and antisymmetric Dzyaloshinsky-Moriya couplings. Quantum coherence is quantified using the recently introduced quantum Jensen-Shannon divergence, which has the property that it is easily calculable and has several desirable mathematical properties. We calculate exactly the coherence for arbitrary number of spins at zero temperature in various limiting cases. The σzσz interaction tunes the amount of coherence in the system, and the antisymmetric coupling changes the nature of the coherence. We also investigate the effect of non-zero temperature by looking at a two-spin system and find similar behavior, with temperature dampening the coherence. The characteristic behavior of coherence resembles that of entanglement and is opposite to that of discord. The distribution of the coherence on the spins is investigated and found that it arises entirely due to the correlations between the spins.
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Affiliation(s)
- Chandrashekar Radhakrishnan
- New York University Shanghai, 1555 Century Ave, Pudong, Shanghai, 200122, China. .,NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China.
| | - Manikandan Parthasarathy
- Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai, 600004, India
| | - Segar Jambulingam
- New York University Shanghai, 1555 Century Ave, Pudong, Shanghai, 200122, China.,Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai, 600004, India
| | - Tim Byrnes
- New York University Shanghai, 1555 Century Ave, Pudong, Shanghai, 200122, China. .,NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China. .,State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai, 200062, China. .,National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan. .,Department of Physics, New York University, New York, NY, 10003, USA.
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19
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Abstract
Quantum coherence plays a major role in the promotion for quantum information processing and designing quantum technology. Since coherence is rooted in superposition principle, it is vital to understand the coherence change with respect to superpositions. Here we study the bounds for coherence of quantum superpositions in high dimension. We consider three most frequently used measures of coherence, i.e. the relative entropy of coherence, l1 norm of coherence and robustness of coherence. For a quantum state (an arbitrary dimension) and its arbitrary decomposition, we give the upper and lower bounds for coherence of the superposition state in terms of the coherence of the states being superposed.
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20
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The classical correlation limits the ability of the measurement-induced average coherence. Sci Rep 2017; 7:45598. [PMID: 28374756 PMCID: PMC5379490 DOI: 10.1038/srep45598] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2017] [Accepted: 02/27/2017] [Indexed: 11/29/2022] Open
Abstract
Coherence is the most fundamental quantum feature in quantum mechanics. For a bipartite quantum state, if a measurement is performed on one party, the other party, based on the measurement outcomes, will collapse to a corresponding state with some probability and hence gain the average coherence. It is shown that the average coherence is not less than the coherence of its reduced density matrix. In particular, it is very surprising that the extra average coherence (and the maximal extra average coherence with all the possible measurements taken into account) is upper bounded by the classical correlation of the bipartite state instead of the quantum correlation. We also find the sufficient and necessary condition for the null maximal extra average coherence. Some examples demonstrate the relation and, moreover, show that quantum correlation is neither sufficient nor necessary for the nonzero extra average coherence within a given measurement. In addition, the similar conclusions are drawn for both the basis-dependent and the basis-free coherence measure.
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21
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The complementarity relations of quantum coherence in quantum information processing. Sci Rep 2017; 7:43919. [PMID: 28272481 PMCID: PMC5341029 DOI: 10.1038/srep43919] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2016] [Accepted: 02/01/2017] [Indexed: 11/09/2022] Open
Abstract
We establish two complementarity relations for the relative entropy of coherence in quantum information processing, i.e., quantum dense coding and teleportation. We first give an uncertainty-like expression relating local quantum coherence to the capacity of optimal dense coding for bipartite system. The relation can also be applied to the case of dense coding by using unital memoryless noisy quantum channels. Further, the relation between local quantum coherence and teleportation fidelity for two-qubit system is given.
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22
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Wang YT, Tang JS, Wei ZY, Yu S, Ke ZJ, Xu XY, Li CF, Guo GC. Directly Measuring the Degree of Quantum Coherence using Interference Fringes. PHYSICAL REVIEW LETTERS 2017; 118:020403. [PMID: 28128592 DOI: 10.1103/physrevlett.118.020403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2016] [Indexed: 06/06/2023]
Abstract
Quantum coherence is the most distinguished feature of quantum mechanics. It lies at the heart of the quantum-information technologies as the fundamental resource and is also related to other quantum resources, including entanglement. It plays a critical role in various fields, even in biology. Nevertheless, the rigorous and systematic resource-theoretic framework of coherence has just been developed recently, and several coherence measures are proposed. Experimentally, the usual method to measure coherence is to perform state tomography and use mathematical expressions. Here, we alternatively develop a method to measure coherence directly using its most essential behavior-the interference fringes. The ancilla states are mixed into the target state with various ratios, and the minimal ratio that makes the interference fringes of the "mixed state" vanish is taken as the quantity of coherence. We also use the witness observable to witness coherence, and the optimal witness constitutes another direct method to measure coherence. For comparison, we perform tomography and calculate l_{1} norm of coherence, which coincides with the results of the other two methods in our situation. Our methods are explicit and robust, providing a nice alternative to the tomographic technique.
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Affiliation(s)
- Yi-Tao Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Jian-Shun Tang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Zhi-Yuan Wei
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Shang Yu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Zhi-Jin Ke
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Xiao-Ye Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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23
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24
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Chitambar E, Hsieh MH. Relating the Resource Theories of Entanglement and Quantum Coherence. PHYSICAL REVIEW LETTERS 2016; 117:020402. [PMID: 27447493 DOI: 10.1103/physrevlett.117.020402] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2015] [Indexed: 06/06/2023]
Abstract
Quantum coherence and quantum entanglement represent two fundamental features of nonclassical systems that can each be characterized within an operational resource theory. In this Letter, we unify the resource theories of entanglement and coherence by studying their combined behavior in the operational setting of local incoherent operations and classical communication (LIOCC). Specifically, we analyze the coherence and entanglement trade-offs in the tasks of state formation and resource distillation. For pure states we identify the minimum coherence-entanglement resources needed to generate a given state, and we introduce a new LIOCC monotone that completely characterizes a state's optimal rate of bipartite coherence distillation. This result allows us to precisely quantify the difference in operational powers between global incoherent operations, LIOCC, and local incoherent operations without classical communication. Finally, a bipartite mixed state is shown to have distillable entanglement if and only if entanglement can be distilled by LIOCC, and we strengthen the well-known Horodecki criterion for distillability.
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Affiliation(s)
- Eric Chitambar
- Department of Physics and Astronomy, Southern Illinois University, Carbondale, Illinois 62901, USA
| | - Min-Hsiu Hsieh
- Centre for Quantum Computation & Intelligent Systems (QCIS), Faculty of Engineering and Information Technology (FEIT), University of Technology Sydney (UTS), Sydney, NSW 2007, Australia
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25
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Hu ML, Fan H. Evolution equation for quantum coherence. Sci Rep 2016; 6:29260. [PMID: 27382933 PMCID: PMC4935996 DOI: 10.1038/srep29260] [Citation(s) in RCA: 72] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2016] [Accepted: 06/13/2016] [Indexed: 01/02/2023] Open
Abstract
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures.
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Affiliation(s)
- Ming-Liang Hu
- School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
| | - Heng Fan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100190, China
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26
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Napoli C, Bromley TR, Cianciaruso M, Piani M, Johnston N, Adesso G. Robustness of Coherence: An Operational and Observable Measure of Quantum Coherence. PHYSICAL REVIEW LETTERS 2016; 116:150502. [PMID: 27127946 DOI: 10.1103/physrevlett.116.150502] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2016] [Indexed: 06/05/2023]
Abstract
Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. Here, the robustness of coherence is defined and proven to be a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is finally provided: the robustness of coherence quantifies the advantage enabled by a quantum state in a phase discrimination task.
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Affiliation(s)
- Carmine Napoli
- Dipartimento di Fisica "E. R. Caianiello", Università degli Studi di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (SA), Italy and INFN Sezione di Napoli, Gruppo Collegato di Salerno, Italy
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Thomas R Bromley
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Marco Cianciaruso
- Dipartimento di Fisica "E. R. Caianiello", Università degli Studi di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (SA), Italy and INFN Sezione di Napoli, Gruppo Collegato di Salerno, Italy
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Marco Piani
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Nathaniel Johnston
- Department of Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick E4L 1E2, Canada
| | - Gerardo Adesso
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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27
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Radhakrishnan C, Parthasarathy M, Jambulingam S, Byrnes T. Distribution of Quantum Coherence in Multipartite Systems. PHYSICAL REVIEW LETTERS 2016; 116:150504. [PMID: 27127948 DOI: 10.1103/physrevlett.116.150504] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2016] [Indexed: 06/05/2023]
Abstract
The distribution of coherence in multipartite systems is examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon divergence. The metric property allows for the coherence to be decomposed into various contributions, which arise from local and intrinsic coherences. We find that there are trade-off relations between the various contributions of coherence, as a function of parameters of the quantum state. In bipartite systems the coherence resides on individual sites or is distributed among the sites, which contribute in a complementary way. In more complex systems, the characteristics of the coherence can display more subtle changes with respect to the parameters of the quantum state. In the case of the XXZ Heisenberg model, the coherence changes from a monogamous to a polygamous nature. This allows us to define the shareability of coherence, leading to monogamy relations for coherence.
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Affiliation(s)
- Chandrashekar Radhakrishnan
- New York University, 1555 Century Avenue, Pudong, Shanghai 200122, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
| | | | - Segar Jambulingam
- Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai 600004, India
| | - Tim Byrnes
- New York University, 1555 Century Avenue, Pudong, Shanghai 200122, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Department of Physics, New York University, New York 10002, USA
- National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
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28
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Hu X, Milne A, Zhang B, Fan H. Quantum coherence of steered states. Sci Rep 2016; 6:19365. [PMID: 26781214 PMCID: PMC4726079 DOI: 10.1038/srep19365] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Accepted: 12/11/2015] [Indexed: 01/04/2023] Open
Abstract
Lying at the heart of quantum mechanics, coherence has recently been studied as a key resource in quantum information theory. Quantum steering, a fundamental notion originally considered by Schödinger, has also recently received much attention. When Alice and Bob share a correlated quantum system, Alice can perform a local measurement to 'steer' Bob's reduced state. We introduce the maximal steered coherence as a measure describing the extent to which steering can remotely create coherence; more precisely, we find the maximal coherence of Bob's steered state in the eigenbasis of his original reduced state, where maximization is performed over all positive-operator valued measurements for Alice. We prove that maximal steered coherence vanishes for quantum-classical states whilst reaching a maximum for pure entangled states with full Schmidt rank. Although invariant under local unitary operations, maximal steered coherence may be increased when Bob performs a channel. For a two-qubit state we find that Bob's channel can increase maximal steered coherence if and only if it is neither unital nor semi-classical, which coincides with the condition for increasing discord. Our results show that the power of steering for coherence generation, though related to discord, is distinct from existing measures of quantum correlation.
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Affiliation(s)
- Xueyuan Hu
- School of Information Science and Engineering, and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Jinan, 250100, P. R. China
| | - Antony Milne
- Controlled Quantum Dynamics Theory, Department of Physics, Imperial College London, London SW7 2AZ, UK
| | - Boyang Zhang
- School of Information Science and Engineering, and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Jinan, 250100, P. R. China
| | - Heng Fan
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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29
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Lostaglio M, Müller MP, Pastena M. Stochastic Independence as a Resource in Small-Scale Thermodynamics. PHYSICAL REVIEW LETTERS 2015; 115:150402. [PMID: 26550711 DOI: 10.1103/physrevlett.115.150402] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Indexed: 06/05/2023]
Abstract
It is well known in thermodynamics that the creation of correlations costs work. It seems then a truism that if a thermodynamic transformation A→B is impossible, so will be any transformation that in sending A to B also correlates among them some auxiliary systems C. Surprisingly, we show that this is not the case for nonequilibrium thermodynamics of microscopic systems. On the contrary, the creation of correlations greatly extends the set of accessible states, to the point that we can perform on individual systems and in a single shot any transformation that would otherwise be possible only if the number of systems involved was very large. We also show that one only ever needs to create a vanishingly small amount of correlations (as measured by mutual information) among a small number of auxiliary systems (never more than three). The many, severe constraints of microscopic thermodynamics are reduced to the sole requirement that the nonequilibrium free energy decreases in the transformation. This shows that, in principle, reliable extraction of work equal to the free energy of a system can be performed by microscopic engines.
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Affiliation(s)
- Matteo Lostaglio
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Markus P Müller
- Department of Applied Mathematics, Department of Philosophy, University of Western Ontario, London, Ontario N6A 5BY, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg, Germany
| | - Michele Pastena
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg, Germany
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