Conditional Decoupling of Quantum Information

Mario Berta, Fernando G. S. L. Brandão, Christian Majenz, and Mark M. Wilde
Phys. Rev. Lett. 121, 040504 – Published 27 July 2018

Abstract

Insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states. In that spirit, Groisman, Popescu, and Winter [Phys. Rev. A 72, 032317 (2005)] showed that the quantum mutual information I(A;B) quantifies the minimal rate of noise needed to erase the correlations in a bipartite state of quantum systems AB. Here, we investigate correlations in tripartite systems ABE. In particular, we are interested in the minimal rate of noise needed to apply to the systems AE in order to erase the correlations between A and B given the information in system E, in such a way that there is only negligible disturbance on the marginal BE. We present two such models of conditional decoupling, called deconstruction and conditional erasure cost of tripartite states ABE. Our main result is that both are equal to the conditional quantum mutual information I(A;B|E)—establishing it as an operational measure for tripartite quantum correlations.

  • Figure
  • Received 7 February 2017
  • Revised 9 January 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.040504

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Mario Berta1,*, Fernando G. S. L. Brandão2, Christian Majenz3,4, and Mark M. Wilde5

  • 1Department of Computing, Imperial College London, London SW7 2AZ, United Kingdom
  • 2Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
  • 3Institute for Language, Logic and Computation, University of Amsterdam and QuSoft, 1098XG Amsterdam, Netherlands
  • 4Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen
  • 5Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA

  • *m.berta@imperial.ac.uk

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Vol. 121, Iss. 4 — 27 July 2018

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