Multi-object operational tasks for measurement incompatibility

TL;DR

This paper introduces multi-object operational tasks to quantify measurement incompatibility in quantum systems, demonstrating how resourceful objects enhance discrimination and exclusion games, with implications extending beyond quantum theory.

Contribution

It presents a novel framework for quantifying measurement incompatibility using multi-object tasks and resource quantifiers, applicable to quantum and general probabilistic theories.

Findings

Resourceful objects improve game performance.

Quantification via robustness and weight of resource.

Results extend beyond quantum to general probabilistic theories.

Abstract

We introduce multi-object operational tasks for measurement incompatibility in the form of multi-object quantum subchannel discrimination and exclusion games with prior information, where a player can simultaneously harness the resources contained within both a quantum state and a set of measurements. We show that any fully or partially resourceful pair of objects is useful for a suitably chosen multi-object subchannel discrimination and exclusion game with prior information. The advantage provided by a fully or partially resourceful object against all possible fully free objects in such a game can be quantified in a multiplicative manner by the resource quantifiers of generalised robustness and weight of resource for discrimination and exclusion games, respectively. These results hold for arbitrary properties of quantum states as well as for arbitrary properties of sets of measurements closed under classical pre and post-processing and, consequently, include measurement incompatibility as a particular case. We furthermore show that these results are not exclusive to quantum theory, but that can also be extended to the realm of general probabilistic theories.