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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Communicated by M. M. Wolf
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Fawzi, O., Renner, R. Quantum Conditional Mutual Information and Approximate Markov Chains. Commun. Math. Phys. 340, 575–611 (2015). https://doi.org/10.1007/s00220-015-2466-x
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DOI: https://doi.org/10.1007/s00220-015-2466-x