Distribution of Interference in the Presence of Decoherence

TL;DR

This paper analyzes how quantum interference behaves in systems interacting with environments, showing that interference diminishes following a power law influenced by environmental temperature and system size.

Contribution

It provides an analytical calculation of the mean and second moment of quantum interference for systems coupled to spin environments, considering unitary evolution from the CUE.

Findings

Interference decays as a power law with system size.

Decay rate depends on environmental temperature.

Analytical expressions for interference moments are derived.

Abstract

We study the statistics of quantum interference for completely positive maps. We calculate analytically the mean interference and its second moment for finite dimensional quantum systems interacting with a simple environment consisting of one or several spins (qudits). The joint propagation of the entire system is taken as unitary with an evolution operator drawn from the Circular Unitary Ensemble (CUE). We show that the mean interference decays with a power law as function of the dimension of the Hilbert space of the environment, with a power that depends on the temperature of the environment.