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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.18803 |
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| _version_ | 1866914052223008768 |
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| author | Chen, Zhixing Chen, Lin |
| author_facet | Chen, Zhixing Chen, Lin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Virtual Quantum Markov Chain of four-qubit systems Chen, Zhixing Chen, Lin Quantum Physics Quantum Algebra 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. |
| title | Virtual Quantum Markov Chain of four-qubit systems |
| topic | Quantum Physics Quantum Algebra |
| url | https://arxiv.org/abs/2509.18803 |