Repeated measurements on non-replicable systems and their consequences for Unruh-DeWitt detectors

TL;DR

This paper develops a framework for predicting measurement outcomes in non-replicable quantum systems using Repeated Measurements, and applies it to Unruh-DeWitt detectors to demonstrate the practical emergence of the Unruh effect.

Contribution

It extends quantum measurement theory to non-replicable systems and shows how RM can approximate Born rule predictions in such contexts, specifically for Unruh-DeWitt detectors.

Findings

RM can approximate Born rule outcomes in non-replicable systems.

Observers can detect the Unruh effect via RM in accelerated detectors.

History-dependent RM probabilities can be close to traditional quantum predictions.

Abstract

The Born rule describes the probability of obtaining an outcome when measuring an observable of a quantum system. As it can only be tested by measuring many copies of the system under consideration, it does not hold for non-replicable systems. For these systems, we give a procedure to predict the future statistics of measurement outcomes through Repeated Measurements (RM). This is done by extending the validity of quantum mechanics to those systems admitting no replicas; we prove that if the statistics of the results acquired by performing RM on such systems is sufficiently similar to that obtained by the Born rule, the latter can be used effectively. We apply our framework to a repeatedly measured Unruh-DeWitt detector interacting with a massless scalar quantum field, which is an example of a system (detector) interacting with an uncontrollable environment (field) for which using RM is necessary. Analysing what an observer learns from the RM outcomes, we find a regime where history-dependent RM probabilities are close to the Born ones. Consequently, the latter can be used for all practical purposes. Finally, we numerically study inertial and accelerated detectors, showing that an observer can see the Unruh effect via RM.