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

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.

7 pages, 1 figure

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• Decoherence and the Nature of System-Environment Correlations
• Lazy states: sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment
• Almost All Quantum States Have Low Entropy Rates for Any Coupling to the Environment
• Pure State Quantum Statistical Mechanics
• Relative purity, speed of fluctuations, and bounds on equilibration times
• A time-dependent Tsirelson's bound from limits on the rate of information gain in quantum systems