How to detect a possible correlation from the information of a sub-system in quantum mechanical systems

TL;DR

This paper demonstrates that correlations between quantum systems can be detected solely from the time-derivative of the reduced purity of a subsystem, providing a practical method for identifying correlations and understanding decoherence.

Contribution

It proves that a non-zero time-derivative of reduced purity indicates correlations and offers a quantitative estimate, advancing the detection of quantum correlations from subsystem information.

Findings

Non-zero time-derivative of reduced purity signals correlations.

Provides a quantitative relation between purity derivative and correlations.

Clarifies the role of correlations in decoherence mechanisms.

Abstract

A possibility to detect correlations between two quantum mechanical systems only from the information of a subsystem is investigated. For generic cases, we prove that there exist correlations between two quantum systems if the time-derivative of the reduced purity is not zero. Therefore, an experimentalist can conclude non-zero correlations between his/her system and some environment if he/she finds the time-derivative of the reduced purity is not zero. A quantitative estimation of a time-derivative of the reduced purity with respect to correlations is also given. This clarifies the role of correlations in the mechanism of decoherence in open quantum systems.