Distributed quantum incompatibility

TL;DR

This paper investigates how adding more measurements affects quantum incompatibility, providing bounds and explicit examples, with implications for nonlocality in Bell experiments.

Contribution

It establishes bounds on the increase of quantum incompatibility with additional measurements and demonstrates their tightness using mutually unbiased bases.

Findings

Bounds on incompatibility increase are tight and explicitly characterized.

Adding measurements can enhance nonlocality in Bell experiments.

Explicit examples based on mutually unbiased bases illustrate the bounds.

Abstract

Incompatible, i.e. non-jointly measurable quantum measurements are a necessary resource for many information processing tasks. It is known that increasing the number of distinct measurements usually enhances the incompatibility of a measurement scheme. However, it is generally unclear how large this enhancement is and on what it depends. Here, we show that the incompatibility which is gained via additional measurements is upper and lower bounded by certain functions of the incompatibility of subsets of the available measurements. We prove the tightness of some of our bounds by providing explicit examples based on mutually unbiased bases. Finally, we discuss the consequences of our results for the nonlocality that can be gained by enlarging the number of measurements in a Bell experiment.