#### Theory Seminar

# Quantum Conditional Mutual Information and Ability to Recover

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The quantum conditional mutual information (QCMI) I(A;C|B) of a tripartite state is meant to qualify the correlations between A and C from the point of view of B. Recently it has found applications in computer science and physics, for example, communication and information complexity, de Finetti type theorems, and also the study of quantum many-body systems.

Despite the fact QCMI can be regarded as the expected mutual information from the point of view of B in classical situations, non-negativity in fully quantum case is a highly nontrivial fact, and it was not proved until 1973. It has become an interesting task since then to find operational importance for QCMI. A recent breakthrough by Fawzi and Renner has successfully related QCMI to recoverability. It has been proved that the less the value I(A;C|B) is, the better C can be recovered from B without knowing C.

There have been several following-up works dealing with recoverability in this year's QIP. It is an interesting fact that many completely different mathematical tools can be exploited to get similar results. In the talk I will briefly introduce the problems being studied in these papers, and try to draw some relation between QCMI with classical computer science problems.