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arXiv · 1904.08852

Communication Cost for Non-Markovianity of Tripartite Quantum States: A Resource Theoretic Approach

Eyuri Wakakuwa
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Abstract

To quantify non-Markovianity of tripartite quantum states from an operational viewpoint, we introduce a class $\Omega^*$ of operations performed by three distant parties. A tripartite quantum state is a free state under $\Omega^*$ if and only if it is a quantum Markov chain. We introduce a function of tripartite quantum states that we call the non-Markovianity of formation, and prove that it is a faithful measure of non-Markovianity, which is continuous and monotonically nonincreasing under a subclass $\Omega$ of $\Omega^*$. We consider a task in which the three parties generate a non-Markov state from scratch by operations in $\Omega$, assisted with quantum communication from the third party to the others, which does not belong to $\Omega$. We prove that the minimum cost of quantum communication required therein is asymptotically equal to the regularized non-Markovianity of formation. Based on this result, we provide a direct operational meaning to a measure of bipartite entanglement called the c-squashed entanglement.

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Eyuri Wakakuwa. 2019-04-18. Communication Cost for Non-Markovianity of Tripartite Quantum States: A Resource Theoretic Approach. https://doi.org/10.1109/tit.2020.3028837

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