Protecting a quantum state from environmental noise by an incompatible finite-time measurement

TL;DR

This paper demonstrates that finite-time quantum measurements can protect a two-state system's initial state from phase noise if the measured observable is incompatible with the environmental interaction, with analytical and numerical validation.

Contribution

It introduces an analytical approximation for the protection mechanism under weak coupling and confirms its validity with exact numerical simulations.

Findings

Finite-time measurements can protect quantum states from environmental noise.

Protection depends on the incompatibility between measured observable and environmental interaction.

Numerical results confirm analytical predictions and show protection beyond weak coupling regimes.

Abstract

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.