Detecting entanglement with Jarzynski’s equality

Hide, Jenny; Vedral, Vlatko

doi:10.1103/physreva.81.062303

Cited by 9 publications

(11 citation statements)

References 23 publications

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“…Recently gave bounds on the entropy production in terms of quantum information concepts. In similar spirit, Hide and Vedral (2010) presented a method by relating relative quantum entropy to the quantum Jarzynski fluctuation identity in order to quantify multi-partite entanglement within different thermal quantum states. A practical application of the Jarzynski equality in quantum computation was showed by Ohzeki (2010).…”

Section: Discussionmentioning

confidence: 99%

Colloquium: Quantum fluctuation relations: Foundations and applications

2011

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Two fundamental ingredients play a decisive role in the foundation of fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars we guide the reader through a self-contained exposition of the theory and applications of quantum fluctuation relations. These are exact results that constitute the fulcrum of the recent development of nonequilibrium thermodynamics beyond the linear response regime. The material is organized in a way that emphasizes the historical connection between quantum fluctuation relations and (non)-linear response theory. We also attempt to clarify a number of fundamental issues which were not completely settled in the prior literature. The main focus is on (i) work fluctuation relations for transiently driven closed or open quantum systems, and (ii) on fluctuation relations for heat and matter exchange in quantum transport settings. Recently performed and proposed experimental applications are presented and discussed. PACS numbers: 05.30.-d, 05.40.-a 05.60.Gg 05.70.Ln, Contents ∞ −∞ e iωs φ BQ (s)ds the Fourier transform of the response function φ BQ (s). Note that the Hänggi and Ingold (2005).

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Section: Discussionmentioning

confidence: 99%

Colloquium: Quantum fluctuation relations: Foundations and applications

2011

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“…Work is defined as the difference between the outcomes of energy measurements near the protocolʼs start and end. This definition of work, which appears in [5,13,15], differs from the definition in [6]. The discrete version of rev ( ) c b e will be defined via analogy with equation (12):…”

Section: Appendix B Quantum Derivation Of Generalized Jarzynski Equamentioning

confidence: 99%

“…This stochasticity necessitates a statistical treatment of work, especially when the deviation from the mean value of work is large. Two popular frameworks employed for this purpose are fluctuation theorems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and one-shot statistical mechanics [16][17][18][19][20][21][22][23]. The former frameworkʼs purpose is to quantify the behaviors of nonequilibrium classical and quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Introducing one-shot work into fluctuation relations

et al. 2015

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Two approaches to small-scale and quantum thermodynamics are fluctuation relations and oneshot statistical mechanics. Fluctuation relations (such as Crooks' theorem and Jarzynskiʼs equality) relate nonequilibrium behaviors to equilibrium quantities such as free energy. One-shot statistical mechanics involves statements about every run of an experiment, not just about averages over trials. We investigate the relation between the two approaches. We show that both approaches feature the same notions of work and the same notions of probability distributions over possible work values. The two approaches are alternative toolkits with which to analyze these distributions. To combine the toolkits, we show how one-shot work quantities can be defined and bounded in contexts governed by Crooks' theorem. These bounds provide a new bridge from one-shot theory to experiments originally designed for testing fluctuation theorems.

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“…In other words, important equilibrium information can be extracted by studying the fluctuations in nonequilibrium work. In recent years, these relations, initially derived for classical systems, have been extended to quantum systems [2,[6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…There is much work on the probability distribution function of the work done [8,10,[13][14][15][16], the thermalization [17], and the quantum entanglement [11,[18][19][20][21][22][23][24] of quantum systems following a quenching. Among them, it is particularly interesting when the change takes the system through a quantum phase transition (QPT) involving macroscopic changes in the state of the system at the initial and final points.…”

Section: Introductionmentioning

confidence: 99%

Work done and irreversible entropy production in a suddenly quenched quantum spin chain with asymmetrical excitation spectra

Zhong

Tong

2015

Phys. Rev. E

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In this paper, we extend the studies on the emergent thermodynamics in a quenched quantum Ising chain (QIC) [R. Dorner, J. Goold, C. Cormick, M. Paternostro, and V. Vedral, Phys. Rev. Lett. 109, 160601 (2012)] to a more general quantum spin chain with asymmetrical excitation spectra. We verify that the Jarzynski and Tasaki-Crooks relations are still tenable in this system. As an example, we discuss the behaviors of the work done and irreversible entropy production induced by a sudden quenching in the anisotropic XY chain in a transverse field with the XZY-YZX type of three-site interactions. Different from the QIC, this system has the phase transitions not only between two gapped phases, but also between gapped (or gapless) and gapless phases at zero temperature. We discuss the effects of quantum phase transitions on the work done and irreversible entropy production at low temperature.

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Detecting entanglement with Jarzynski’s equality

Cited by 9 publications

References 23 publications

Colloquium: Quantum fluctuation relations: Foundations and applications

Colloquium: Quantum fluctuation relations: Foundations and applications

Introducing one-shot work into fluctuation relations

Work done and irreversible entropy production in a suddenly quenched quantum spin chain with asymmetrical excitation spectra

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