Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution

• Main Authors: Brandao, Fernando G. S. L (Author), Harrow, Aram W. (Contributor), Oppenheim, Jonathan (Author), Strelchuk, Sergii (Author)
• Other Authors: Massachusetts Institute of Technology. Center for Theoretical Physics (Contributor), Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2015-07-30T11:54:12Z.
• Subjects: Article
• Online Access: Get fulltext

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.
National Science Foundation (U.S.) (Grant CCF-1111382)
National Science Foundation (U.S.) (Grant CCF-1452616)
United States. Army Research Office (Contract W911NF-12-1-0486)
Leverhulme Trust