Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival

TL;DR

This paper investigates how to accurately measure the quantum time of arrival despite the quantum Zeno effect by normalizing measurement outcomes, revealing a classical-like distribution.

Contribution

It introduces a normalization method for repeated quantum measurements that uncovers the true time distribution despite the Zeno effect.

Findings

Normalizing measurement data reveals a classical-like time distribution.

The method overcomes the wave reflection caused by frequent measurements.

An ideal quantum time of arrival distribution is obtained.

Abstract

Repeated measurements of a quantum particle to check its presence in a region of space was proposed long ago [G. R. Allcock, Ann. Phys. {\bf 53}, 286 (1969)] as a natural way to determine the distribution of times of arrival at the orthogonal subspace, but the method was discarded because of the quantum Zeno effect: in the limit of very frequent measurements the wave function is reflected and remains in the original subspace. We show that by normalizing the small bits of arriving (removed) norm, an ideal time distribution emerges in correspondence with a classical local-kinetic-energy distribution.