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Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution

Brandão, Fernando G. S. L. and Harrow, Aram W. and Oppenheim, Jonathan and Strelchuk, Sergii (2015) Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution. Physical Review Letters, 115 (5). Art. No. 050501. ISSN 0031-9007. doi:10.1103/PhysRevLett.115.050501.

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We give two strengthenings of an inequality for the quantum conditional mutual information of a tripartite quantum state recently proved by Fawzi and Renner, connecting it with the ability to reconstruct the state from its bipartite reductions. Namely, we show that the conditional mutual information is an upper bound on the regularized relative entropy distance between the quantum state and its reconstructed version. It is also an upper bound for the measured relative entropy distance of the state to its reconstructed version. The main ingredient of the proof is the fact that the conditional mutual information is the optimal quantum communication rate in the task of state redistribution.

Item Type:Article
Related URLs:
URLURL TypeDescription Material
Brandão, Fernando G. S. L.0000-0003-3866-9378
Harrow, Aram W.0000-0003-3220-7682
Oppenheim, Jonathan0000-0002-8993-412X
Additional Information:© 2015 American Physical Society. (Received 29 December 2014; published 29 July 2015) F. G. S. L. B. and J. O. thank EPSRC for financial support. A. W. H. was funded by NSF Grants No. CCF-1111382 and CCF-1452616, ARO Contract No. W911NF-12-1-0486, and a grant from the Leverhulme Trust. S. S. acknowledges the support of Sidney Sussex College. We thank Omar Fawzi, Ke Li, Marco Tomamichel, Mark Wilde, and Lin Zhang for helpful comments and the Newton Institute for their hospitality while some of this research was conducted.
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Army Research Office (ARO)W911NF-12-1-0486
Leverhulme TrustUNSPECIFIED
Sidney Sussex CollegeUNSPECIFIED
Issue or Number:5
Classification Code:PACS numbers: 03.67.Mn
Record Number:CaltechAUTHORS:20160607-105210912
Persistent URL:
Official Citation:Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution Fernando G. S. L. Brandão, Aram W. Harrow, Jonathan Oppenheim, and Sergii Strelchuk Phys. Rev. Lett. 115, 050501
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67723
Deposited By: George Porter
Deposited On:07 Jun 2016 18:21
Last Modified:11 Nov 2021 03:53

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