Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity

• URL: http://arxiv.org/abs/2504.16165v1
• Date: Tue, 22 Apr 2025 18:00:02 GMT
• Title: Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity
• Authors: Seunghun Lee, Eun-Gook Moon,
• Abstract summary: We investigate 1D and 2D cluster states under local decoherence to assess the robustness of their mixed-state subsystem symmetry-protected topological order.<n>We show that mixed-state SSPT order remains remarkably robust up to the maximal decoherence rate when noise respects strong subsystem symmetry.
• Score: 2.8391355909797644
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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