Relaxation and Zeno effect in qubit measurements

TL;DR

This paper derives Bloch-type equations for a monitored qubit interacting with its environment, showing how measurement and noise spectra reveal decoherence and relaxation, and demonstrating that environmental interaction prevents perfect qubit localization.

Contribution

It introduces a comprehensive model with Bloch equations for a qubit, environment, and detector, providing new analytical expressions for measurement-related quantities.

Findings

Detector current and noise spectrum relate to qubit decoherence and relaxation rates.

Measurement cannot fully localize a qubit due to environmental interaction.

Analytical expressions enable accurate measurement of decoherence and relaxation.

Abstract

We consider a qubit interacting with its environment and continuously monitored by a detector represented by a point contact. Bloch-type equations describing the entire system of the qubit, the environment and the detector are derived. Using these equations we evaluate the detector current and its noise spectrum in terms of the decoherence and relaxation rates of the qubit. Simple expressions are obtained that show how these quantities can be accurately measured. We demonstrate that due to interaction with the environment, the measurement can never localize a qubit even for infinite decoherence rate.