A trace condition Tr(T(R))=1 on the logarithmic junction-tree construction exactly determines existence and uniqueness of quantum Markov completions for density operators, coinciding with the maximum-entropy state.
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The Markov Marginal Problem for Density Operators
A trace condition Tr(T(R))=1 on the logarithmic junction-tree construction exactly determines existence and uniqueness of quantum Markov completions for density operators, coinciding with the maximum-entropy state.