Measurement-Induced Indistinguishability and the Limits of Post-Processing

Description (Abstract): > This paper formalizes a minimal impossibility result concerning information recovery under constrained observation. Given an observation map ϕ:M→F that is not injective, we show that there exist intrinsic indistinguishability classes in M whose elements cannot be distinguished by any post-processing applied after, regardless of computational power, model complexity, or stochastic processing. The result clarifies a fundamental boundary between observation and post-processing that is often implicit but rarely stated explicitly across dynamical systems, information processing, and representation learning.