Beyond Zeno: Approaching Infinite Temperature upon Repeated Measurements

TL;DR

This paper investigates how repeated quantum measurements affect a system's state, revealing a transition in the approach rate to a uniform state from smooth to erratic as measurement intervals vary.

Contribution

It introduces a detailed analysis of the dynamics of quantum systems under repeated measurements, highlighting a sharp transition in the approach rate to infinite temperature.

Findings

Approaching a uniform state becomes exponential with finite Hilbert space.

The rate of approach exhibits a sharp transition from monotonic to erratic behavior.

Repeated measurements can drive the system towards an infinite temperature state.

Abstract

The influence of repeated projective measurements on the dynamics of the state of a quantum system is studied in dependence of the time lag $\tau$ between successive measurements. In the limit of infinitely many measurements of the occupancy of a single state the total system approaches a uniform state. The asymptotic approach to this state is exponential in the case of finite Hilbert space dimension. The rate characterizing this approach undergoes a sharp transition from a monotonically increasing to an erratically varying function of the time between subsequent measurements.