Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution

TL;DR

This paper strengthens an inequality relating quantum conditional mutual information to the ability to reconstruct quantum states, linking it to quantum communication rates in state redistribution.

Contribution

It introduces two new bounds connecting quantum conditional mutual information with the fidelity of state reconstruction, enhancing understanding of quantum state recoverability.

Findings

Conditional mutual information bounds the reconstructed state's distance from the original.

The bounds relate to both relative entropy and measured relative entropy.

Conditional mutual information equals the optimal quantum communication rate in 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 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.