Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity
This paper demonstrates that mixed-state subsystem symmetry-protected topological order in cluster states remains robust up to maximal decoherence rates when noise respects strong subsystem symmetry, and proposes "spurious topological entanglement negativity" as a constant correction to area-law scaling for detecting this order while highlighting the non-invariance of standard topological entanglement negativity under finite-depth quantum channels.