Communications in Mathematical Physics

, Volume 328, Issue 1, pp 251–284

One-Shot Decoupling

  • Frédéric Dupuis
  • Mario Berta
  • Jürg Wullschleger
  • Renato Renner
Open Access
Article

Abstract

If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears (almost) completely, resulting in a decoupling of A from E. We give a criterion for decoupling in terms of two smooth entropies, one quantifying the amount of initial correlation between A and E, and the other characterizing the mapping that describes the evolution of A. The criterion applies to arbitrary such mappings in the general one-shot setting. Furthermore, the criterion is tight for mappings that satisfy certain natural conditions. One-shot decoupling has a number of applications both in physics and information theory, e.g., as a building block for quantum information processing protocols. As an example, we give a one-shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption/production.

Copyright information

© The Author(s) 2014

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  • Frédéric Dupuis
    • 1
  • Mario Berta
    • 1
  • Jürg Wullschleger
    • 2
    • 3
  • Renato Renner
    • 1
  1. 1.Institute for Theoretical PhysicsETH ZurichZurichSwitzerland
  2. 2.Department of Computer Science and Operations ResearchUniversité de MontréalMontrealCanada
  3. 3.McGill UniversityMontrealCanada

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