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arXiv · 2507.15262

Multipartite Markov Gaps and Entanglement Wedge Multiway Cuts

Norihiro Iizuka·Akihiro Miyata·Mitsuhiro Nishida
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Abstract

The Markov gap, defined as the difference between reflected entropy and mutual information, serves as a diagnostic for quantum recoverability and multipartite entanglement. In holographic settings, it admits a geometric interpretation as the deviation between entanglement wedge cross-sections and RT surfaces. Motivated by this holographic perspective, we propose a generalization of the Markov gap to multipartite systems by using a reflected multi-entropy. The resulting Multipartite Markov gap can capture geometric obstructions to bulk reconstruction. We investigate the properties of this quantity from both information-theoretic and holographic viewpoints, and examine its potential operational significance through candidate recovery maps. We further introduce the genuine reflected multi-entropy, which is designed to vanish for states containing only lower-partite entanglement. Together, these quantities offer complementary probes of recoverability and multipartite structure in holographic quantum systems.

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Norihiro Iizuka, Akihiro Miyata, Mitsuhiro Nishida. 2025-07-21. Multipartite Markov Gaps and Entanglement Wedge Multiway Cuts. https://arxiv.org/abs/2507.15262

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