Estimation of the Repeatedly-Projected Reduced Density Matrix under Decoherence

TL;DR

This paper derives an analytic expression for the reduced density matrix of a two-qubit system under decoherence, showing that pure states can still be extracted despite environmental effects, especially with dephasing or finite measurements.

Contribution

It provides a novel analytic framework for understanding purification under decoherence, highlighting conditions for successful pure state extraction.

Findings

Pure states can be extracted under dephasing environments.

Finite measurements can yield dominant pure states in dissipative environments.

Analytic expression for the reduced density matrix under decoherence.

Abstract

Decoherence is believed to deteriorate the ability of a purification scheme that is based on the idea of driving a system to a pure state by repeatedly measuring another system in interaction with the former and hinder for a pure state to be extracted asymptotically. Nevertheless, we find a way out of this difficulty by deriving an analytic expression of the reduced density matrix for a two-qubit system immersed in a bath. It is shown that we can still extract a pure state if the environment brings about only dephasing effects. In addition, for a dissipative environment, there is a possibility of obtaining a dominant pure state when we perform a finite number of measurements.