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.

Questo articolo esplora i giri e le loro implicazioni.

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