A contextual advantage for conclusive exclusion: repurposing the Pusey-Barrett-Rudolph construction

TL;DR

This paper demonstrates a quantum advantage in conclusive exclusion tasks using a construction inspired by the Pusey-Barrett-Rudolph theorem, with implications for noncontextuality and causal compatibility.

Contribution

It introduces a new quantum advantage in conclusive exclusion, derives noise-robust inequalities, and links the results to classical causal models and the PBR construction.

Findings

Quantum advantage in conclusive exclusion demonstrated.

Derived noise-robust noncontextuality inequalities.

Violations imply a quantum-classical gap in causal scenarios.

Abstract

The task of conclusive exclusion for a set of quantum states is to find a measurement such that for each state in the set, there is an outcome that allows one to conclude with certainty that the state in question was not prepared. Defining classicality of statistics as realizability by a generalized-noncontextual ontological model, we show that there is a quantum-over-classical advantage for how well one can achieve conclusive exclusion. This is achieved in an experimental scenario motivated by the construction appearing in the Pusey-Barrett-Rudolph theorem. We derive noise-robust noncontextuality inequalities bounding the conclusiveness of exclusion, and describe a quantum violation of these. Finally, we show that this bound also constitutes a classical causal compatibility inequality within the bilocality scenario, and that its violation in quantum theory yields a novel possibilistic proof of a quantum-classical gap in that scenario.