Double Markovity for quantum systems
Quantum Physics
2026-01-16 v1
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.
Cite
@article{arxiv.2601.09995,
title = {Double Markovity for quantum systems},
author = {Masahito Hayashi and Jinpei Zhao},
journal= {arXiv preprint arXiv:2601.09995},
year = {2026}
}