Oscillations of the purity in the repeated-measurement-based generation of quantum states

TL;DR

This paper investigates how the purity of a quantum system evolves under repeated measurements, revealing oscillations that can temporarily reduce purity before reaching a pure state.

Contribution

It provides a detailed analysis of purity oscillations during measurement-induced state preparation, highlighting conditions that cause temporary purity dips.

Findings

Purity can oscillate and dip below initial levels during state evolution.

Oscillations depend on measurement parameters and system interactions.

Final state purity approaches unity regardless of initial mixedness.

Abstract

Repeated observations of a quantum system interacting with another one can drive the latter toward a particular quantum state, irrespectively of its initial condition, because of an {\em effective non-unitary evolution}. If the target state is a pure one, the degree of purity of the system approaches unity, even when the initial condition of the system is a mixed state. In this paper we study the behavior of the purity from the initial value to the final one, that is unity. Depending on the parameters, after a finite number of measurements, the purity exhibits oscillations, that brings about a lower purity than that of the initial state, which is a point to be taken care of in concrete applications.