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arXiv · 1410.0664

Quantum conditional mutual information and approximate Markov chains

Omar Fawzi·Renato Renner
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Abstract

A state on a tripartite quantum system $A \otimes B \otimes C$ forms a Markov chain if it can be reconstructed from its marginal on $A \otimes B$ by a quantum operation from $B$ to $B \otimes C$. We show that the quantum conditional mutual information $I(A: C | B)$ of an arbitrary state is an upper bound on its distance to the closest reconstructed state. It thus quantifies how well the Markov chain property is approximated.

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Omar Fawzi, Renato Renner. 2015-01-21. Quantum conditional mutual information and approximate Markov chains. https://doi.org/10.1007/s00220-015-2466-x

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