Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution

Understand

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 regularised 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.