How contextuality and antidistinguishability are related

TL;DR

This paper explores the relationship between quantum contextuality and antidistinguishability, establishing that contextuality implies weak antidistinguishability and introducing a resource-based perspective on both properties.

Contribution

It formalizes the connection between contextuality and antidistinguishability, extending traditional notions and treating both as resources in quantum information theory.

Findings

Contextual sets are necessarily weakly antidistinguishable.

Critical contextuality is a stronger resource than traditional antidistinguishability.

A formal relationship links the degree of contextuality to antidistinguishability levels.

Abstract

Contextuality is a key characteristic that separates quantum from classical phenomena and an important tool in understanding the potential advantage of quantum computation. However, when assessing the quantum resources available for quantum information processing, there is no formalism to determine whether a set of states can exhibit contextuality and whether such proofs of contextuality indicate anything about the resourcefulness of that set. Introducing a well-motivated notion of what it means for a set of states to be contextual, we establish a relationship between contextuality and antidistinguishability of sets of states. We go beyond the traditional notions of contextuality and antidistinguishability and treat both properties as resources, demonstrating that the degree of contextuality within a set of states has a direct connection to its level of antidistinguishability. If a set of states is contextual, then it must be weakly antidistinguishable and vice-versa. However, critical contextuality emerges as a stronger property than traditional antidistinguishability.