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 and non-classicality of quantum Markov processes
TL;DR: In this paper, it was shown that quantum coherence is not equivalent to non-classicality in the sense that it cannot be traced back to a classical statistics if and only if the dynamics is able to generate coherences and to subsequently turn them into populations.
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Extracting quantum coherence via steering.
Xueyuan Hu,Heng Fan +1 more
TL;DR: In this paper, the authors established an operational connection between coherence induced by steering and the quantum correlation and showed that the steering-induced coherence quantified by such as relative entropy of coherence and trace-norm of co-herence is bounded from above by a known quantum correlation measure defined as the one-side measurement-induced disturbance.
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All Quantum Resources Provide an Advantage in Exclusion Tasks.
TL;DR: In this paper, it was shown that the convex weight of any quantum resource corresponds exactly to the relative advantage it offers in an exclusion (or antidistinguishability) task.
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Assessing the quantumness of a damped two-level system
TL;DR: In this paper, a detailed analysis of the nonclassical properties of a damped two-level system was performed and three different criteria of quantumness, including the norm of coherence, the Leggett-Garg inequality, and a quantum witness based on the no-signaling in time condition were compared.
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Ordering states with coherence measures
TL;DR: In this paper, the authors consider the two well-known coherence measures, the $$l_1$$l1 norm of coherence and the relative entropy of Coherence, and show that there are the states for which the two measures give a different ordering.
References
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TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
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TL;DR: In this article, a rigorous framework for quantification of coherence and identification of intuitive and easily computable measures for coherence has been proposed by adopting coherence as a physical resource.