Virtual Quantum Markov Chain of four-qubit systems
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.
Keywords
Cite
@article{arxiv.2509.18803,
title = {Virtual Quantum Markov Chain of four-qubit systems},
author = {Zhixing Chen and Lin Chen},
journal= {arXiv preprint arXiv:2509.18803},
year = {2025}
}