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arXiv · 2509.18803

Virtual Quantum Markov Chain of four-qubit systems

Zhixing Chen·Lin Chen
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Abstract

We extend the framework of virtual quantum Markov chains (VQMCs) from tripartite systems to the four-qubit setting. Structural criteria such as the kernel-inclusion condition are analyzed, showing that they are necessary but not sufficient for the existence of a valid recovery map. By explicit examples, we demonstrate that the four-qubit W state admits a recovery channel and thus qualifies as a VQMC, while the GHZ state does not. We further provide semidefinite programming (SDP) formulations to test recoverability and quantify sampling overhead, and establish the non-convexity of the VQMC set through mixed-state counterexamples. These results supply both theoretical insights and computational tools for studying correlations and recoverability in multipartite quantum systems.

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Zhixing Chen, Lin Chen. 2025-09-23. Virtual Quantum Markov Chain of four-qubit systems. https://arxiv.org/abs/2509.18803

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