The asymmetry properties of pure quantum states

TL;DR

This paper investigates the asymmetry properties of pure quantum states relative to symmetry groups, revealing their characterization via characteristic functions and exploring implications for state transformations under symmetric dynamics.

Contribution

It introduces a characterization of pure state asymmetry using characteristic functions and applies this to analyze state interconversion under symmetric quantum dynamics.

Findings

Pure state asymmetry is fully characterized by the state's characteristic function.

Conditions for reversible and irreversible state transformations under symmetry are established.

Insights into asymptotic state transformations are provided.

Abstract

The asymmetry properties of a state relative to some symmetry group specify how and to what extent the given symmetry is broken by the state. Characterizing these is found to be surprisingly useful for addressing a very common problem: to determine what follows from a system's dynamics (possibly open) having that symmetry. We demonstrate and exploit the fact that the asymmetry properties of a state can be understood in terms of information-theoretic concepts. We show that for a pure state psi and a symmetry group G, they are completely specified by the characteristic function of the state, defined as chi_psi(g)=<psi|U(g)|psi> where g\in G and U is the unitary representation of interest. Based on this observation, we study several important problems about the interconversion of pure states under symmetric dynamics such as determining the conditions for reversible transformations, deterministic irreversible transformations and asymptotic transformations.