Distillation by repeated measurements: continuous spectrum case

TL;DR

This paper explores how repeated measurements can induce state distillation in quantum systems with continuous spectra, extending previous results from discrete spectra and demonstrating the process with a simple model.

Contribution

It generalizes the concept of measurement-induced distillation to systems with continuous spectra, providing a formalism and validation through a simple model.

Findings

Effective distillation occurs even with continuous spectra under general conditions.

Repeated measurements influence unmeasured parts via an effective evolution operator.

The formalism is validated with a specific quantum model.

Abstract

Repeated measurements on a part of a bipartite system strongly affect the other part not measured, whose dynamics is regulated by an effective contracted evolution operator. When the spectrum of this operator is discrete, the latter system is driven into a pure state irrespective of the initial state, provided the spectrum satisfies certain conditions. We here show that even in the case of continuous spectrum an effective distillation can occur under rather general conditions. We confirm it by applying our formalism to a simple model.