Information-Theoretic Uncertainty Relation and Random-Phase Entropy

TL;DR

This paper investigates the behavior of entropy in quantum Gaussian wave packets, proposing that the random-phase entropy monotonically increases regardless of the classicality of the states, challenging previous assumptions.

Contribution

It introduces the concept that random-phase entropy always increases monotonically, extending the understanding of entropy dynamics beyond maximally classical states.

Findings

Joint entropy does not always increase monotonically for general Gaussian wave packets.

Random-phase entropy consistently increases monotonically for various Gaussian states.

Challenges previous results that only considered maximally classical states.

Abstract

Dunkel and Trigger [Phys. Rev. A {71}, 052102 (2005)] show that the Leipnik's joint entropy monotonously increases for the initially maximally classical Gaussian wave packet for a free particle. After expressing the joint entropy of the general Gaussian wave packets for quadratic Hamiltonians as $S (t) = ln (e/2) + ln (2 Delta x (t) Delta p (t)/hbar)$, we show that a class of general Gaussian wave packets does not warrant the monotonous increase of the joint entropy. We propose that the random-phase entropy with respect to the squeeze angle always monotonously increases even for non-maximally classical states.