On evolution of maximally-classical states

A. Montina, Stefan Wolf

The Leggett-Garg inequalities were originally intro-duced for experimentally testing a possible break of the quantum evolution in meso scopic systems. In this paper, we take a different point of view by focusing on faithful classical simulations of sequential quantum measurements. In this context, the violation of Leggett-Garg inequalities implies that classically simulated quantum measurements induce perturbations into the subsequent evolution of the classical variables. We show that the implication is even stronger and a measurement erases previous information by performing a partial reset on the classical state. Thus, the measuring device acts as a low-temperature bath absorbing entropy from the measured system. Information erasure is a form of preparation contextuality. Our proof is straightforward if one assumes that maximal ignorance of the quantum state is compatible with maximal ignorance of the classical state. We also employ a weaker hypothesis.

Alexander Wilce

Piotr Garbaczewski

In the above-mentioned paper by Dunkel and Trigger [Phys. Rev. A 71, 052102 (2005)] a hypothesis has been pursued that the loss of information associated with the quantum evolution of pure states, quantified in terms of an increase in the time of so-called Leipnik's joint entropy, could be a rather general property shared by many quantum systems. This behavior has been confirmed for the unconfined model systems and properly tuned initial data (maximally classical states). We provide two particular examples which indicate a complexity of the quantum evolution. In the presence of a confining (harmonic) potential Leipnik's entropy there may be nonincreasing for maximally classical initial data. Another choice of initial data implies periodicity in the time of the Leipnik entropy.

F. A. Popp

Jeremy Storm

Tomasz Linowski, Łukasz Rudnicki

The notion of classicality of quantum evolution of light is an object of both conceptual and practical importance. The main goal of this work is to derive the exact conditions for the classicality of quantum Gaussian evolution, i.e., the evolution of Gaussian states of light and their convex combinations, a model which is of great significance in quantum optics and information. According to our findings, quantum Gaussian evolution should be considered classical if the Hamiltonian and Lindblad operators generating it correspond to passive optical transformations. This is illustrated with several explicit examples, ranging from Gaussian thermal operations to entanglement-maximizing dissipative engineering. Our results are obtained using the recently introduced mesoscopic formalism of the reduced state of the field, which was originally devised as as a description of macroscopic quantum fields. Here, to make the framework suitable for our goal, we redevelop it as a tool for probing classicality, which constitutes our second main contribution.