Irreversibility, Information and Randomness in Quantum Measurements

TL;DR

This paper analyzes quantum measurement irreversibility through quantum information theory, showing that information about purity isn't transferred during measurement, leading to outcomes consistent with the Born rule, regardless of decoherence effects.

Contribution

It demonstrates that quantum-mechanical constraints prevent transfer of purity information, explaining measurement randomness and confirming the Born rule without decoherence altering these results.

Findings

Information about purity isn't transferred during measurement.

Measurement outcomes follow the Born rule.

Decoherence effects do not change the fundamental results.

Abstract

Irreversibility in quantum measurements is considered from the point of quantum information theory. For that purpose the information transfer between the measured object S and measuring system O is analyzed. It's found that due to the principal constraints of quantum-mechanical origin, the information about the purity of S state isn't transferred to O during the measurement of arbitraryS observable V. Consequently O can't discriminate the pure and mixed S ensembles with the same <V>. As the result, the random outcomes should be detected by O in V measurement for S pure ensemble of V eigenstate superposition. It's shown that the outcome probabilties obey to Born rule. The influence of O decoherence by its environment is studied, however the account of its effects doesn't change these results principally.