A Gaussian asymmetry measure

TL;DR

This paper introduces a Gaussian-based asymmetry measure for quantum states that remains within the Gaussian manifold, enabling exact computation and capturing key dynamical features like the Mpemba effect.

Contribution

It proposes a new Gaussian asymmetry measure that avoids non-Gaussian complexities and can be computed exactly using correlation matrices.

Findings

The measure quantifies the minimal distance to symmetric Gaussian states.

It captures dynamical signatures such as the Mpemba effect and symmetry restoration.

The measure can be described asymptotically via the quasiparticle picture.

Abstract

The study of Entanglement Asymmetry has emerged in recent years as a powerful tool to characterise the symmetry properties of quantum states in relation to a given charge operator through the lens of entanglement. While extremely powerful and general, the standard definition of asymmetry introduces significant non-Gaussian features in free-fermionic systems, leading to certain analytical limitations. In this work, we introduce an asymmetry measure that remains strictly within the Gaussian manifold and analyse its properties. In particular, we show that it quantifies the minimal distance between a Gaussian state and the manifold of symmetric Gaussian states. We further demonstrate that this measure captures the established dynamical signatures of entanglement asymmetry, such as the Mpemba effect, symmetry restoration, and the lack thereof. The Gaussian structure allows these novel asymmetry measures to be computed exactly using correlation matrix techniques, and to be described asymptotically through the quasiparticle picture. We also comment on the possibility of using charge fluctuations to characterise the asymmetry of a Gaussian state.