Probabilistic Distillation of Quantum Coherence

Fang, Kun; Wang, Xin; Lami, Ludovico; Regula, Bartosz; Adesso, Gerardo

doi:10.1103/physrevlett.121.070404

Cited by 93 publications

(88 citation statements)

References 46 publications

(106 reference statements)

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“…The state conversion problem is important in any resource theory, since it determines the value of states for protocols using the resource under study. The result presented here are a significant generalization of recent results on single-shot coherence theory [10,[23][24][25][26] and single-shot resource theories in general [27], and include necessary conditions on the existence of stochastic conversions, which we generalized to higher dimensions.…”

Section: Discussionmentioning

confidence: 53%

Quantum coherence and state conversion: theory and experiment

Theurer

Xiang

et al. 2020

npj Quantum Inf

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The resource theory of coherence [1-6] studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion [3, 7-10] of the resource. Here we solve this question completely for qubit states by determining the optimal probabilities for mixed state conversions via stochastic incoherent operations. Extending the discussion to distributed scenarios, we introduce and address the task of assisted incoherent state conversion where the process is enhanced by making use of correlations with a second party. Building on these results, we demonstrate experimentally that the optimal state conversion probabilities can be achieved in a linear optics set-up. This paves the way towards real world applications of coherence transformations in current quantum technologies.Practical constraints on our ability to manipulate physical systems restrict the control we can exert on them. It is, for example, exceedingly difficult to exchange quantum systems undisturbed over long distances [11]. When manipulating spatially separated subsystems, effectively, this limits us to Local Operations and Classical Communication (LOCC). Under these operations, it is only possible to prepare certain states, i.e. separable ones. The states which cannot be produced under LOCC are called entangled and elevated to resources: Consuming them allows to implement operations such as quantum state teleportation [12] to achieve perfect quantum state transfer which would not be possible with LOCC alone. This has important consequences, e.g. in quantum communication and other quantum technologies, but also for our understanding of the view of the fundamental laws of nature [11,[13][14][15].Entanglement is explored within the framework of quantum resource theories, which can also be used to investigate other non-classical features of quantum mechanics in a systematic way. A concept underlying many * These authors contributed equally to this work. †

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Section: Discussionmentioning

confidence: 53%

Quantum coherence and state conversion: theory and experiment

Theurer

Xiang

et al. 2020

npj Quantum Inf

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“…Third, as our method provides an estimation of the spectrum, it can be used to estimate any Schur-convex or Schurconcave quantities, such as the purity, Tsallis entropy, and Rényi entropy. The method can also be used for estimating other coherence measures [11,21,[65][66][67][68]. More details are reported in Appendix D, in which some novel relations between different coherence measures are also proposed.…”

Section: Multi-partite Systemsmentioning

confidence: 99%

Detecting coherence via spectrum estimation

Gühne

2019

Phys. Rev. A

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Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to measure the coherence in experiments limits the applications. We address this problem by introducing an experiment-friendly method for coherence and spectrum estimation. This method is based on the theory of majorization and can not only be used to prove the presence of coherence, but also result in a rather precise lower bound of the amount of coherence. As an illustration, we show how to characterize the freezing phenomenon of coherence with only two local measurements for any N-qubit quantum systems. Our approach also has other applications in quantum information processing, such as the characterization of distillability and entanglement transformations. * Xiao-Dong.Yu@uni-siegen.de † otfried.guehne@uni-siegen.de

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“…Concentration of measure states that a function that depends in a Lipschitz way on many independent variables is almost constant. As a special form of concentration of measure, Levy's lemma is commonly used in the typicality related literature [14,44,45]. Here we compare the distribution of the GWvN entropy S Eq.…”

Section: Appendix A: Concentration Of Measure and Levy's Lemmamentioning

confidence: 99%

“…Unfortunately, we now know that macroscopic objects are made of microscopic particles that obey the laws of quantum mechanics. It is therefore desirable and imperative to understand the second law in the perspective of quantum dynamics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Generalized Wigner–von Neumann entropy and its typicality

Wang

2019

Phys. Rev. E

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We propose a generalization of the quantum entropy introduced by Wigner and von Neumann [Zeitschrift für Physik 57, 30 (1929)]. Our generalization is applicable to both quantum pure states and mixed states. When the dimension N of the Hilbert space is large, this generalized Wigner-von Neumann (GWvN) entropy becomes independent of choices of basis and is asymptotically equal to ln N in the sense of typicality. The dynamic evolution of our entropy is also typical, reminiscent of quantum H theorem proved by von Neumann. For a composite system, the GWvN entropy is typically additive; for the microcanonical ensemble, it is equivalent to the Boltzmann entropy; for a system entangled with environment, it is consistent with the familiar von Neumann entropy, which is zero for pure states. In addition, the GWvN entropy can be used to derive the Gibbs ensemble.

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Probabilistic Distillation of Quantum Coherence

Cited by 93 publications

References 46 publications

Quantum coherence and state conversion: theory and experiment

Quantum coherence and state conversion: theory and experiment

Detecting coherence via spectrum estimation

Generalized Wigner–von Neumann entropy and its typicality

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