Resource theory of coherence: Beyond states

Khaled Ben Dana, María García Díaz, Mohamed Mejatty, and Andreas Winter
Phys. Rev. A 95, 062327 – Published 20 June 2017; Erratum Phys. Rev. A 96, 059903 (2017)

Abstract

We generalize the recently proposed resource theory of coherence (or superposition) [T. Baumgratz et al., Phys. Rev. Lett. 113, 140401 (2014); A. Winter and D. Yang, Phys. Rev. Lett. 116, 120404 (2016)] to the setting where not just the free (“incoherent”) resources, but also the manipulated objects, are quantum operations rather than states. In particular, we discuss an information theoretic notion of the coherence capacity of a quantum channel and prove a single-letter formula for it in the case of unitaries. Then we move to the coherence cost of simulating a channel and prove achievability results for unitaries and general channels acting on a d-dimensional system; we show that a maximally coherent state of rank d is always sufficient as a resource if incoherent operations are allowed, and one of rank d2 for “strictly incoherent” operations. We also show lower bounds on the simulation cost of channels that allow us to conclude that there exists bound coherence in operations, i.e., maps with nonzero cost of implementing them but zero coherence capacity; this is in contrast to states, which do not exhibit bound coherence.

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  • Received 21 April 2017

DOI:https://doi.org/10.1103/PhysRevA.95.062327

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Erratum

Erratum: Resource theory of coherence: Beyond states [Phys. Rev. A 95, 062327 (2017)]

Khaled Ben Dana, María García Díaz, Mohamed Mejatty, and Andreas Winter
Phys. Rev. A 96, 059903 (2017)

Authors & Affiliations

Khaled Ben Dana1,*, María García Díaz2,†, Mohamed Mejatty1,‡, and Andreas Winter2,3,§

  • 1Laboratory of Advanced Materials and Quantum Phenomena, Department of Physics, Faculty of Sciences of Tunis, University Tunis El Manar, Tunis 2092, Tunisia
  • 2Departament de Física: Grup d'Informació Quàntica, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain
  • 3ICREA—Institució Catalana de Recerca i Estudis Avançats, Pg. Lluís Companys, 23, ES-08001 Barcelona, Spain

  • *khaled.bendana@gmail.com
  • maria.garciadia@e-campus.uab.cat
  • mohamedmejatty@yahoo.fr
  • §andreas.winter@uab.cat

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Issue

Vol. 95, Iss. 6 — June 2017

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