Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution
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PhysRevLett.115.050501.pdf
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Author(s)
Brandao, Fernando G. S. L.
Harrow, Aram W.
Oppenheim, Jonathan
Strelchuk, Sergii
Date Issued
July 2015
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Brandao, Fernando G. S. L., Aram W. Harrow, Jonathan Oppenheim, and Sergii Strelchuk. "Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution." Phys. Rev. Lett. 115, 050501 (July 2015). © 2015 American Physical Society
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.115.050501
