Time-of-arrival correlations

TL;DR

This paper introduces a new approach to measuring time-of-arrival correlations in quantum systems, demonstrating their potential to distinguish different theoretical models and serve as entanglement witnesses.

Contribution

It constructs a novel POVM for bipartite time-of-arrival measurements, showing these correlations differ from traditional probability currents and can detect entanglement.

Findings

Time-of-arrival correlations differ from probability current-based probabilities.

Time-of-arrival correlations can serve as entanglement witnesses.

A new state-reduction rule for time-of-arrival measurements is derived.

Abstract

We propose that measurements of time-of-arrival correlations in multi-partite systems can sharply distinguish between different approaches to the time-of-arrival problem. To show this, we construct a Positive-Operator-Valued measure for two distinct time-of-arrival measurements in a bipartite system, and we prove that the resulting probabilities differ strongly from ones defined in terms of probability currents. We also prove that time-of-arrival correlations are entanglement witnesses, a result suggesting the use of temporal observables for quantum information processing tasks. Finally, we construct the probabilities for sequential time-of-arrival measurements on a single particle. We derive the state-reduction rule for time-of-arrival measurements; it differs significantly from the standard one, because time-of-arrival measurements are not defined at a single predetermined moment of time.