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arXiv · 2601.09995

Double Markovity for quantum systems

Masahito Hayashi·Jinpei Zhao
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Abstract

The subadditivity-doubling-rotation (SDR) technique is a powerful route to Gaussian optimality in classical information theory and relies on strict subadditivity and its equality-case analysis, where double Markovity is a standard tool. We establish quantum analogues of double Markovity. For tripartite states, we characterize the simultaneous Markov conditions A-B-C and A-C-B via compatible projective measurements on B and C that induce a common classical label J yielding A-J-(BC). For strictly positive four-party states, we show that A-(BD)-C and A-(CD)-B hold if and only if A-D-(BC) holds. These results remove a key bottleneck in extending SDR-type arguments to quantum systems.

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Masahito Hayashi, Jinpei Zhao. 2026-01-15. Double Markovity for quantum systems. https://arxiv.org/abs/2601.09995

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