Local enhancement of finite-strength code preparation: recoverability and Wilson coherence

arXiv:2611.14967v1 Announce Type: new Abstract: Stabilizer measurements provide a direct route to preparing quantum error-correcting codes and long-range entangled states. In realistic implementations, however, finite measurement strength can coherently deform the encoding map away from the projective limit. Certain nonlocal signatures associated with long-range order can survive such a deformation, but this alone does not guarantee that the resulting state protects encoded quantum information. We show that, at fixed strength, local logical leakage obstructs asymptotically faithful recovery; along logical operators' supports, its accumulation forces the relevant measurement strength to grow logarithmically with code distance.