On the computational complexity of detecting possibilistic locality

TL;DR

This paper investigates the computational complexity of determining possibilistic nonlocality in quantum systems, focusing on how the problem's difficulty varies with measurement outcomes and providing insights into the computational boundaries of quantum nonlocality detection.

Contribution

It introduces the complexity analysis of possibilistic locality detection, identifying the specific conditions under which the problem becomes computationally hard.

Findings

The problem is computationally easy for certain measurement configurations.

The problem becomes NP-hard when one party has two outcomes and the other three.

Provides a complexity boundary for possibilistic nonlocality detection.

Abstract

The proofs of quantum nonlocality due to GHZ and Hardy are quantitatively different from that of Bell insofar as they rely only on a consideration of whether events are possible or impossible, rather than relying on specific experimental probabilities. Here, we consider the computational task of determining whether or not a given table of possibilities constitutes a departure from possibilistic local realism. By considering the case in which one party has access to measurements with two outcomes and the other three, it is possible to see at exactly which point this task becomes computationally difficult.