Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution.
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.
Department of Computer Science, University College London, Gower St, London WC1E 6BT, UK and Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052-6399, USA.
Fernando G S L
FG
Brandão
Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Aram W
AW
Harrow
Department of Physics, University College London, Gower St, London WC1E 6BT, UK.
Jonathan
J
Oppenheim
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.
Sergii
S
Strelchuk