Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity

Abstract:We investigate 1D and 2D cluster states under local decoherence to assess the robustness of their mixed-state subsystem symmetry-protected topological (SSPT) order. By exactly computing fidelity correlators via dimensional reduction of effective statistical mechanics models, we pinpoint the critical error rate for strong-to-weak spontaneous breaking of strong subsystem symmetry. Without resorting to the replica trick, we demonstrate that mixed-state SSPT order remains remarkably robust up to the maximal decoherence rate when noise respects strong subsystem symmetry. Furthermore, we propose that the mixed-state SSPT order can be detected by a constant correction to the area-law scaling of entanglement negativity, termed spurious topological entanglement negativity. This also highlights that topological entanglement negativity, a widely used diagnostic for mixed-state topological order, is generally not invariant under finite-depth quantum channels.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2504.16165 [quant-ph]

(or arXiv:2504.16165v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2504.16165 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. B 112, L161121 (2025)

https://doi.org/10.1103/g9bs-s562 Focus to learn more DOI(s) linking to related resources

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