Discord and Decoherence

TL;DR

This paper explores how quantum discord, a measure of quantum correlations, evolves during decoherence in Gaussian systems and applies these insights to cosmological perturbations, linking quantum and classical behaviors.

Contribution

It introduces a generic parametrization for system partitioning and analyzes the competition between squeezing growth and purity loss affecting quantum discord.

Findings

Quantum discord evolution depends on squeezing amplitude and state purity.

In phase space, discord changes relate to the Wigner ellipse geometry.

Application to cosmology shows how quantum fluctuations become classical structures.

Abstract

In quantum information theory, quantum discord has been proposed as a tool to characterise the presence of "quantum correlations" between the subparts of a given system. Whether a system behaves quantum-mechanically or classically is believed to be impacted by the phenomenon of decoherence, which originates from the unavoidable interaction between this system and an environment. Generically, decoherence is associated with a decrease of the state purity, i.e. a transition from a pure to a mixed state. In this paper, we investigate how quantum discord is modified by this quantum-to-classical transition. This study is carried out on systems described by quadratic Hamiltonians and Gaussian states, with generalised squeezing parameters. A generic parametrisation is also introduced to describe the way the system is partitioned into two subsystems. We find that the evolution of quantum discord in presence of an environment is a competition between the growth of the squeezing amplitude and the decrease of the state purity. In phase space, this corresponds to whether the semi-minor axis of the Wigner ellipse increases or decreases, which has a clear geometrical interpretation. Finally, these considerations are applied to primordial cosmological perturbations, thus allowing us to investigate how large-scale structures in our universe, which are believed to arise from quantum fluctuations, can exhibit classical properties.