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Published July 31, 2015 | Supplemental Material + Published
Journal Article Open

Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution

Abstract

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.

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.

Attached Files

Published - PhysRevLett.115.050501.pdf

Supplemental Material - FR-PRL-Appendix.pdf

Supplemental Material - FR-PRL-Appendix.tex

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August 20, 2023
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