Focusing in Arthurs-Kelly-type Joint Measurements with Correlated Probes

TL;DR

This paper extends the Arthurs-Kelly joint measurement model to include entangled and correlated probes, demonstrating improved measurement precision without violating Heisenberg's uncertainty principle.

Contribution

It introduces a generalized Arthurs-Kelly model with correlated probes, showing enhanced measurement accuracy while maintaining quantum uncertainty constraints.

Findings

Correlated probes can yield more precise joint measurements of position and momentum.

The measured observable remains covariant under phase space translations.

No violations of Heisenberg's measurement uncertainty relations occur in the extended model.

Abstract

Joint approximate measurement schemes of position and momentum provide us with a means of inferring pieces of complementary information if we allow for the irreducible noise required by quantum theory. One such scheme is given by the Arthurs-Kelly model, where information about a system is extracted via indirect probe measurements. So far, only separable uncorrelated probes have been considered. Here, following Di Lorenzo (PRL 110, 120403 (2013)), we extend this model to both entangled and classically correlated probes, achieving full generality. We find the measured observable of the system under consideration to be covariant under phase space translations, and show that correlated probes can produce more precise joint measurement outcomes of position and momentum than the same probes can achieve if applied alone to realize a position or momentum measurement. Contrary to Di Lorenzo's claim, we find that nevertheless there are no violations of Heisenberg's measurement uncertainty relations in these generalized Arthurs-Kelly models.