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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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2
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De Chiara G, Sanpera A. Genuine quantum correlations in quantum many-body systems: a review of recent progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:074002. [PMID: 29671752 DOI: 10.1088/1361-6633/aabf61] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.
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Affiliation(s)
- Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
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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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Streltsov A, Chitambar E, Rana S, Bera MN, Winter A, Lewenstein M. Entanglement and Coherence in Quantum State Merging. PHYSICAL REVIEW LETTERS 2016; 116:240405. [PMID: 27367369 DOI: 10.1103/physrevlett.116.240405] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2016] [Indexed: 06/06/2023]
Abstract
Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging, where two parties aim to merge their tripartite quantum state parts. In standard quantum state merging, entanglement is considered to be an expensive resource, while local quantum operations can be performed at no additional cost. However, recent developments show that some local operations could be more expensive than others: it is reasonable to distinguish between local incoherent operations and local operations which can create coherence. This idea leads us to the task of incoherent quantum state merging, where one of the parties has free access to local incoherent operations only. In this case the resources of the process are quantified by pairs of entanglement and coherence. Here, we develop tools for studying this process and apply them to several relevant scenarios. While quantum state merging can lead to a gain of entanglement, our results imply that no merging procedure can gain entanglement and coherence at the same time. We also provide a general lower bound on the entanglement-coherence sum and show that the bound is tight for all pure states. Our results also lead to an incoherent version of Schumacher compression: in this case the compression rate is equal to the von Neumann entropy of the diagonal elements of the corresponding quantum state.
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Affiliation(s)
- A Streltsov
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, D-14195 Berlin, Germany
| | - E Chitambar
- Department of Physics and Astronomy, Southern Illinois University, Carbondale, Illinois 62901, USA
| | - S Rana
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain
| | - M N Bera
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain
| | - A Winter
- Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, ES-08010 Barcelona, Spain
| | - M Lewenstein
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, ES-08010 Barcelona, Spain
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Sadhukhan D, Roy SS, Rakshit D, Prabhu R, Sen De A, Sen U. Quantum discord length is enhanced while entanglement length is not by introducing disorder in a spin chain. Phys Rev E 2016; 93:012131. [PMID: 26871048 DOI: 10.1103/physreve.93.012131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2015] [Indexed: 06/05/2023]
Abstract
Classical correlation functions of ground states typically decay exponentially and polynomially, respectively, for gapped and gapless short-range quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an information-theoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XYZ spin glass and random field chains. We find that there is virtually neither reduction nor enhancement in entanglement length while quantum discord length increases significantly with the introduction of the quenched disorder.
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Affiliation(s)
- Debasis Sadhukhan
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Sudipto Singha Roy
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Debraj Rakshit
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - R Prabhu
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Aditi Sen De
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Ujjwal Sen
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
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