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arXiv · 1709.07248

Operational Resource Theory of Non-Markovianity

Eyuri Wakakuwa
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Abstract

In order to analyze non-Markovianity of tripartite quantum states from a resource theoretical viewpoint, we introduce a class of quantum operations performed by three distant parties, and investigate an operational resource theory (ORT) induced it. A tripartite state is a free state if and only if it is a quantum Markov chain. We prove monotonicity of functions such as the conditional quantum mutual information, intrinsic information, squashed entanglement, a generalization of entanglement of purification, and the relative entropy of recovery. The ORT has five bound sets, each of which corresponds to one of the monotone functions. We introduce a task of "non-Markovianity dilution", and prove that the optimal rate for the task, namely the "non-Markovianity cost", is bounded from above by entanglement of purification in the case of pure states. We also propose a classical resource theory of non-Markovianity.

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Eyuri Wakakuwa. 2017-09-21. Operational Resource Theory of Non-Markovianity. https://arxiv.org/abs/1709.07248

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