• Open Access

One-Shot Manipulation of Dynamical Quantum Resources

Bartosz Regula and Ryuji Takagi
Phys. Rev. Lett. 127, 060402 – Published 5 August 2021
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Abstract

We develop a unified framework to characterize one-shot transformations of dynamical quantum resources in terms of resource quantifiers, establishing universal conditions for exact and approximate transformations in general resource theories. Our framework encompasses all dynamical resources represented as quantum channels, including those with a specific structure—such as boxes, assemblages, and measurements—thus immediately applying in a vast range of physical settings. For the particularly important manipulation tasks of distillation and dilution, we show that our conditions become necessary and sufficient for broad classes of important theories, enabling an exact characterization of these tasks and establishing a precise connection between operational problems and resource monotones based on entropic divergences. We exemplify our results by considering explicit applications to quantum communication, where we obtain exact expressions for one-shot quantum capacity and simulation cost assisted by no-signaling, separability-preserving, and positive partial transpose–preserving codes; as well as to nonlocality, contextuality, and measurement incompatibility, where we present operational applications of a number of relevant resource measures.

  • Received 29 January 2021
  • Accepted 21 June 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.060402

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Bartosz Regula1,*,† and Ryuji Takagi1,2,*,‡

  • 1School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
  • 2Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *Both authors contributed equally to this work.
  • bartosz.regula@gmail.com
  • ryuji.takagi@ntu.edu.sg

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Issue

Vol. 127, Iss. 6 — 6 August 2021

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