Fidelity, quantum computations and Wilson loop

TL;DR

This paper explores the relationship between quantum fidelity decay and Wilson loops in QCD, analyzing how symmetries influence the stability and statistical properties of quantum systems interacting with stochastic environments.

Contribution

It demonstrates the analogy between quantum fidelity and Wilson loops, deriving decay rates and analyzing symmetry effects across different physical systems.

Findings

Fidelity decay rates are derived for various systems.

Symmetry groups significantly influence system stability.

The similarity between fidelity and Wilson loops is established.

Abstract

General properties of quantum systems which interact with stochastic environment are studied with a strong emphasis on the role of physical symmetries. The similarity between the fidelity which is used to characterize the stability of such a systems and the Wilson loop in QCD is demonstrated, and the fidelity decay rates are derived. The consequences of existence of the symmetry group on the statistical properties of the system are analyzed for various physical systems - a simple quantum mechanical system, holonomic quantum computer and Yang-Mills fields.