Quantum contextuality with mixed states of 1D symmetry-protected topological order

Quantum Physics [Submitted on 13 Mar 2026] Quantum contextuality with mixed states of 1D symmetry-protected topological order Leroy Fagan, Akimasa Miyake Bell theorems of many-body nonlocality and contextuality serve as a benchmark for proving quantum advantage in that a quantum computer outperforms a classical computer for a certain problem. In practice, however, near-term quantum devices do not prepare perfectly pure states but rather mixed states produced from noisy channels. We investigate noisy quantum advantage by considering thermal mixed states of one-dimensional many-body systems with a symmetry-protected topological (SPT) order. In the pure-state (or zero-temperature) case, these states are known to be useful for measurement-based quantum computation, and to outperform classical computers in a many-body contextuality game, provided string order parameters (SOPs) of SPT are sufficiently large. Here, we show that quantum advantage in mixed states is measured by a combination of twisted SOP and symmetry representation expectation values. Using the minimally entangled typical thermal states algorithm, it is demonstrated that quantum advantage persists to a nonzero critical temperature for finite-sized instances of the many-body contextuality game. While this critical temperature goes to zero in the thermodynamic limit, it is relatively robust to system size, suggesting that these states remain useful for demonstrating genuine "quantumness" of noisy hardware in a scalable fashion. Finally, we show that the quantum winning probability is lower bounded by the global fidelity with the 1D cluster state, so that our contextuality game can provide an operational meaning to benchmark the capacity to create long-range order like SPT states in near-term experimental devices. Comments: 15 pages + 6 pages supplemental material, 7 + 2 figures Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2603.13626 [quant-ph]   (or arXiv:2603.13626v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.13626 Focus to learn more Submission history From: Leroy Fagan [view email] [v1] Fri, 13 Mar 2026 22:13:14 UTC (3,369 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.str-el References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)