Postselection-Free Reconstruction of Monitored SPT Flux-Charge Responses

• URL: http://arxiv.org/abs/2608.15477v1
• Date: Sun, 16 Aug 2026 01:52:10 GMT
• Title: Postselection-Free Reconstruction of Monitored SPT Flux-Charge Responses
• Abstract summary: A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical records.<n>We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder.
• Score: 1.599072005190786
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical stochastic records, so direct estimation requires exponentially costly matched-record postselection. We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder. Their correlation yields an exact finite-time response identity and removes this experimental sampling bottleneck. When the ordinary charge sharpens and the ordinary-to-flux deformation has trivial net readout-character flow, the response converges to the projective commutator of the symmetry-protected-topological phase; generator-pair responses then determine its finite-Abelian cohomology class. Spectator-sector crossings may close the global Lyapunov gap without changing this character-valued response. In monitored cluster circuits, the decoder is exact and polynomial in the Gaussian limit, while Gaussian-drop reconstruction treats interacting records; independent joint-sector spectroscopy and effect-state diagnostics validate the topological deformation.

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