Conditional mutual information and quantum steering

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...

Renyi generalizations of the conditional quantum mutual information

The conditional quantum mutual information I(A;B|C) of a tripartite state ρABC is an information quantity which lies at the center of many problems in quantum information theory. Three of its main properties are that it is non-negative for any tripartite state, that it decreases under local operations applied to systems A and B, and that it obeys the duality relation I(A;B|C) = I(A;B|D) for a f...

Directed Information and Conditional Mutual Information

—We study directed information in Bayesian networks and related structures. Mutual information is split into directed information and residual information. Some basic equations for directed information and residual information are determined.

The Intrinsic Conditional Mutual Information

This paper is concerned with secret key agreement by public discussion: two parties Alice and Bob and an adversary Eve have access to independent realizations of random variables X, Y , and Z, respectively, with joint distribution P XY Z. The secret key rate S(X; Y jjZ) has been deened as the maximal rate at which Alice and Bob can generate a secret key by communication over an insecure, but au...

About the Mutual (Conditional) Information