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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Coherence measure: Logarithmic coherence number
Zhengjun Xi,Shanshan Yuwen +1 more
TL;DR: The logarithmic coherence number as mentioned in this paper is a measure of coherence which is extended from the coherence rank via the standard convex roof construction; it is parallel to the Schmidt measure in entanglement theory.
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The classical correlation limits the ability of the measurement-induced average coherence.
TL;DR: It is shown that the average coherence is not less than the coherence of its reduced density matrix and the classical correlation of the bipartite state instead of the quantum correlation is neither sufficient nor necessary for the nonzero extra average coherent within a given measurement.
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Maximal Steered Coherence and Its Conversion to Entanglement in Multiple Bosonic Reservoirs
Xiao-Xiao Xu,Ming-Liang Hu +1 more
Journal ArticleDOI
Quantum coherence as a signature of chaos
TL;DR: In this article, the authors propose connections between the resource theory of quantum coherence and various signatures of chaotic quantum systems, and make use of these signatures to construct a model of quantum systems.
Journal ArticleDOI
One-shot entanglement distillation beyond local operations and classical communication
TL;DR: In this paper, the authors study the problem of entanglement distillation in the one-shot setting under different classes of quantum operations which extend the set of local operations and classical communication (LOCC).
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