Quantum stroboscopy for time measurements

TL;DR

This paper introduces quantum stroboscopic measurements, a method that uses repeated position measurements on different system copies to accurately determine a particle's time of arrival, overcoming the limitations posed by the quantum Zeno effect.

Contribution

The paper proposes a novel quantum measurement scheme called quantum stroboscopy, which allows for accurate time-of-arrival measurements by combining projective measurements on different system copies, bypassing Mielnik's argument.

Findings

Quantum stroboscopy reproduces conventional time-of-arrival statistics.

It can describe general and conditional time measurements.

The method overcomes the quantum Zeno effect limitations.

Abstract

Mielnik's cannonball argument uses the Zeno effect to argue that projective measurements for time of arrival are impossible. If one repeatedly measures the position of a particle (or a cannonball!) that has yet to arrive at a detector, the Zeno effect will repeatedly collapse its wavefunction away from it: the particle never arrives. Here we introduce quantum stroboscopic measurements where we accumulate statistics of projective position measurements, performed on different copies of the system at different times, to obtain a time-of-arrival distribution. We show that, under appropriate limits, this gives the same statistics as time measurements of conventional ``always on'' particle detectors, that bypass Mielnik's argument using non-projective, weak continuous measurements. In addition to time of arrival, quantum stroboscopy can describe distributions of general time measurements. It can also be adapted to obtain the conditional probability distribution of arrival times, given that the particle was not previously detected at the detector.