Stochastic Quantum Zeno by Large Deviation Theory

TL;DR

This paper investigates the effects of random-time projective measurements on quantum systems, demonstrating how large deviation theory can predict survival probabilities and enhance quantum state protection through stochastic measurement sequences.

Contribution

It introduces an analytical framework using large deviation theory to analyze quantum Zeno effects under random measurement intervals, providing new insights into quantum state preservation.

Findings

Survival probability follows a large-deviation form with many measurements.

Disorder in measurement timing can increase survival probability.

Analytical results confirmed by numerical tests on entangled states.

Abstract

Quantum measurements are crucial to observe the properties of a quantum system, which however unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system while being subject to a sequence of projective measurements applied at random times. In the case of independent and identically distributed intervals of time between consecutive measurements, we analytically demonstrate that the survival probability of the system to remain in the projected state assumes a large-deviation (exponentially decaying) form in the limit of an infinite number of measurements. This allows us to estimate the typical value of the survival probability, which can therefore be tuned by controlling the probability distribution of the random time intervals. Our analytical results are numerically tested for Zeno-protected entangled states, which also demonstrates that the presence of disorder in the measurement sequence further enhances the survival probability when the Zeno limit is not reached (as it happens in experiments). Our studies provide a new tool for protecting and controlling the amount of quantum coherence in open complex quantum systems by means of tunable stochastic measurements.