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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Benchmarking one-shot distillation in general quantum resource theories
TL;DR: In this article, a set of tools applicable to broad classes of resource theories is developed, revealing the similarities among many of them and establishing universal limitations on the distillation of such resources in practical settings.
Journal ArticleDOI
When Is a Non-Markovian Quantum Process Classical?
Simon Milz,Simon Milz,Dario Egloff,Dario Egloff,Philip Taranto,Thomas Theurer,Martin B. Plenio,Andrea Smirne,Andrea Smirne,Andrea Smirne,Susana F. Huelga +10 more
TL;DR: A new paradigm for separating what is inherently quantum from what is classical relies solely on observable quantities and makes it possible to identify the mechanisms leading to nonclassicality in a wide range of situations as discussed by the authors.
Journal ArticleDOI
Duality Games and Operational Duality Relations.
TL;DR: A tight wave-particle duality relation is found that allows us to relate the probabilities of winning these games, and use it to find an upper bound on the probability of winning the combined game.
Journal ArticleDOI
Deterministic Coherence Distillation.
C. L. Liu,Duan-Lu Zhou +1 more
TL;DR: This Letter finds the necessary and sufficient condition for the transformation from a mixed coherent state into a pure state via strictly incoherent operations, which recovers a connection between the resource theory of coherence and the algebraic theory of majorization lattice.
Journal ArticleDOI
Quantifying quantum speedups: improved classical simulation from tighter magic monotones
James R. Seddon,Bartosz Regula,Hakop Pashayan,Hakop Pashayan,Hakop Pashayan,Yingkai Ouyang,Earl T. Campbell +6 more
TL;DR: This work proposes three different classical algorithms for simulating universal quantum circuits and connects each algorithm's performance to a corresponding magic monotone and, by comprehensively characterizing the monotones, gets a precise understanding of the simulation runtime and error bounds.
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.