Two Quantum Paradigms, but Still No Signal
Samuel Epstein
TL;DR
The paper examines how classical information emerges (or fails to) under two quantum-measurement paradigms: the Copenhagen/POVM approach and decoherence with einselection. It develops an information-theoretic and algorithmic framework, showing that for most quantum states, POVM outcomes carry negligible self-information and decoherence drives states toward algorithmic white noise, limiting extractable signals. By introducing an algorithmic predictability sieve, it demonstrates that pointer states can carry high a priori signal, but almost all states collapse into noise that cannot be exploited, due to fundamental information-conservation inequalities in the algorithmic sense. The work highlights a fundamental barrier to obtaining usable signals from generic quantum states and clarifies the special role of pointer states and environmental selection in classicalizaton.
Abstract
An overwhelming majority of quantum (pure and mixed) states, when undertaking a POVM measurement, will result in a classical probability with no algorithmic information. Thus most quantum states produce white noise when measured. Furthermore most non-pointer states, when undergoing the decoherence process, will produce white noise. These results can be seen as consequences of the vastness of Hilbert spaces.