What question did this study set out to answer?

To explore the limits of information recovery from observations that are not injective, highlighting the challenges in distinguishability.

January 18, 2026Open Access

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Measurement-Induced Indistinguishability and the Limits of Post-Processing

TSTak Heung Sze

Key Points

To explore the limits of information recovery from observations that are not injective, highlighting the challenges in distinguishability.
Formal analysis of observation maps and their injectivity properties.
Identification of indistinguishability classes and their characteristics.
Examination of the impacts of computational power and model complexity on information recovery.
Demonstrated that certain indistinguishability classes cannot be distinguished regardless of post-processing methods.
Clarified the boundary between observation and post-processing in various systems.
Found that constraints in observation fundamentally limit information recovery.

Abstract

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.

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Cite This Study

Tak Heung Sze (Fri,) studied this question.

synapsesocial.com/papers/696c7817eb60fb80d13963ee https://doi.org/https://doi.org/10.5281/zenodo.18274146

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