Joint measurements through quantum broadcasting

TL;DR

This paper investigates the possibility of generating joint quantum measurements via broadcasting channels, identifying conditions under which this is feasible, especially for local sharp and noisy observables, and exploring resourcefulness in measurement scenarios.

Contribution

It provides necessary and sufficient conditions for broadcasting-based joint measurements, extending understanding of quantum measurement compatibility and resourcefulness.

Findings

Broadcasting can generate joint measurements for local sharp observables under certain dominance conditions.

Impossible to generate joint measurements of continuous sharp observables through broadcasting.

Characterized resourcefulness of local measurements in combined broadcasting, measurement, and post-processing scenarios.

Abstract

We study generating joint measurements by operating on the input quantum state with a broadcasting channel followed by local measurements on the two outputs of the broadcasting channel. Although, due to perfect broadcasting or cloning being impossible, this scheme cannot generate perfect joint observables for all pairs of quantum observables, we study for what intended joint observables and local measurements this procedure can be carried out. For local sharp observables this is always possible as long as the intended joint observable is dominated by the tensor product of the local sharp observables. This result excludes the case of joint measurements of continuous sharp observables with themselves which we indeed show to be impossible to be generated through broadcasting. We also derive necessary and sufficient conditions for the success of the broadcasting scheme for local noisy observables and intended joint observables which are easily checked when the local observables are convex mixtures of sharp observables and white noise. We also study broadcasting of local fuzzy observables in the presence of symmetries. Finally we introduce the scenario of measuring joint observables where we have access to broadcasting, local measurements and post-processing and characterize the most resourceful local measurements in this setting.