Measurement-only circuits realize gapless SPT phases with nontrivial edge states at criticality, including symmetry-enriched percolation in Ising models and persistent Z4 gSPT phases mapped to Majorana loop models.
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Monitored random quantum circuits lack divergent multipartite entanglement at criticality unlike standard critical systems, but two-site measurements with a protection mechanism enable genuinely multipartite entangled phases.
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Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
Measurement-only circuits realize gapless SPT phases with nontrivial edge states at criticality, including symmetry-enriched percolation in Ising models and persistent Z4 gSPT phases mapped to Majorana loop models.
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Multipartite entanglement structure of monitored quantum circuits
Monitored random quantum circuits lack divergent multipartite entanglement at criticality unlike standard critical systems, but two-site measurements with a protection mechanism enable genuinely multipartite entangled phases.