The quantum Zeno and anti-Zeno effects with non-selective measurements

TL;DR

This paper develops a formalism to analyze the quantum Zeno and anti-Zeno effects under non-selective measurements, revealing significant differences from traditional selective measurement approaches especially beyond weak coupling regimes.

Contribution

It introduces a general formalism for non-selective measurements in quantum Zeno studies and demonstrates its impact on decay dynamics in various solvable models.

Findings

Non-selective measurements can significantly alter Zeno and anti-Zeno effects.

Differences between selective and non-selective measurement scenarios become prominent beyond weak coupling.

The formalism applies to models like dephasing and spin systems, showing varied decay behaviors.

Abstract

In studies of the quantum Zeno and anti-Zeno effects, it is usual to consider rapid projective measurements with equal time intervals being performed on the system to check whether or not the system is in the initial state. These projective measurements are selective measurements in the sense that the measurement results are read out and only the case where all the measurement results correspond to the initial state is considered in the analysis of the effect of the measurements. In this paper, we extend such a treatment to consider the effect of repeated non-selective measurements - only the final measurement is required to correspond to the initial state, while we do not know the results of the intermediate measurements. We present a general formalism to derive the effective decay rate of the initial quantum state with such non-selective measurements. Importantly, we show that there is a difference between using non-selective measurements and the usual approach of considering only selective measurements only if we go beyond the weak system-environment coupling regime in models other than the usual population decay models. As such, we then apply our formalism to investigate the quantum Zeno and anti-Zeno effects for three exactly solvable system-environment models: a single two-level system undergoing dephasing, a single two-level system interacting with an environment of two-level systems, and a large spin undergoing dephasing. Our results show that the quantum Zeno and anti-Zeno effects in the presence of non-selective measurements can differ very significantly as compared to the repeated selective measurement scenario.