Quantum properties of a non-Gaussian state in the large-N approximation

TL;DR

This paper investigates the quantum properties of a non-Gaussian state in an O(N) scalar field, revealing how non-Gaussian correlators influence effective descriptions and quantum coherence in large-N regimes.

Contribution

It provides an exact calculation of the non-Gaussian density matrix at leading order in 1/N, highlighting the impact on quantum properties like purity and entropy.

Findings

Gaussian and non-Gaussian observers may agree on purity but differ on coherence.

Exact matrix elements enable analysis of strong non-Gaussianity effects.

Non-Gaussian correlators significantly alter effective quantum descriptions.

Abstract

We study the properties of a non-Gaussian density matrix for a O(N) scalar field in the context of the incomplete description picture. This is of relevance for studies of decoherence and entropy production in quantum field theory. In particular, we study how the inclusion of the simplest non-Gaussian correlator in the set of measured observables modifies the effective (Gaussian) description one can infer from the knowledge of the two-point functions only. We compute exactly the matrix elements of the non-Gaussian density matrix at leading order in a 1/N-expansion. This allows us to study the quantum properties (purity, entropy, coherence) of the corresponding state for arbitrarily strong nongaussianity. We find that if the Gaussian and the non-Gaussian observers essentially agree concerning quantum purity or correlation entropy, their conclusion can significantly differ for other, more detailed aspects such as the degree of quantum coherence of the system.