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Operational Resource Theory of Coherence

Andreas Winter and Dong Yang
Phys. Rev. Lett. 116, 120404 – Published 24 March 2016
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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.

  • Received 10 July 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.120404

© 2016 American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

Andreas Winter1,2,* and Dong Yang2,3,†

  • 1ICREA—Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys, 23, ES-08010 Barcelona, Spain
  • 2Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain
  • 3Laboratory for Quantum Information, China Jiliang University, Hangzhou, Zhejiang 310018, China

  • *andreas.winter@uab.cat
  • dyang@cjlu.edu.cn

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Issue

Vol. 116, Iss. 12 — 25 March 2016

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