Operational Resource Theory of Coherence.
TLDR
An operational theory of coherence (or of superposition) in quantum systems is established, by focusing on the optimal rate of performance of certain tasks, by demonstrating that the coherence theory is generically an irreversible theory by a simple criterion that completely characterizes all reversible states.Abstract:
We establish an operational theory of coherence (or of superposition) in quantum systems, by focusing on the optimal rate of performance of certain tasks. Namely, we introduce the two basic concepts-"coherence distillation" and "coherence cost"-in the processing quantum states under so-called incoherent operations [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. We, then, show that, in the asymptotic limit of many copies of a state, both are given by simple single-letter formulas: the distillable coherence is given by the relative entropy of coherence (in other words, we give the relative entropy of coherence its operational interpretation), and the coherence cost by the coherence of formation, which is an optimization over convex decompositions of the state. An immediate corollary is that there exists no bound coherent state in the sense that one would need to consume coherence to create the state, but no coherence could be distilled from it. Further, we demonstrate that the coherence theory is generically an irreversible theory by a simple criterion that completely characterizes all reversible states.read more
Citations
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Quantifying quantum coherence based on the Tsallis relative operator entropy
TL;DR: In this paper, a family of coherence quantifiers based on the Tsallis relative operator entropy is presented. But the quantifiers do not satisfy all the standard criteria for a well-defined measure of quantum coherence and include some existing coherence measures as special cases.
Journal ArticleDOI
Coherence non-activating measurement
TL;DR: In this article, a connection is built between the coherence activating ability of a measurement and its ability to steer quantum states when coherence non-activating measurements are allowed, and the quantum discord is studied based on the quantum nonactivating measurement and the behavior under local incoherent operations.
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General measure for macroscopic quantum states beyond "dead and alive"
TL;DR: In this paper, a measure based on mutual information is proposed to characterize the distinguishability between multiple superposition states, which is applicable to superpositions of multiple macroscopically distinct states.
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Quantifying Unsharpness of Observables in an Outcome-Independent way
TL;DR: In this article , an instrument-independent unsharpness measure is defined via uncertainty and does not depend on the values of the outcomes, which is consistent with the resource-theoretic framework.
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