Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables

TL;DR

This paper introduces a quantum contextuality framework involving mutually complementary observables organized into pseudocontexts, revealing how quantum and classical models differ in probability bounds and explaining the nature of quantum contextuality.

Contribution

It presents a novel quantum system with pseudocontexts and analyzes how quantum bounds on probabilities differ from classical models, highlighting the role of contextuality.

Findings

Quantum systems with pseudocontexts have state-independent probability sums.

Quantum bounds on linear probability combinations can be violated by classical models.

Classical ontological models cannot replicate the quantum probability bounds.

Abstract

We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases within the Hilbert space, featuring a state-independent sum of probabilities. In other words, regardless of the initial state preparation, the total probability remains constant but may be distinct from unity. The measurement contextuality in this setup arises from the quantum realizations of the hypergraph, which adhere to a specific bound on the linear combination of probabilities. In contrast, classical realizations can surpass this bound. The violation of quantum bounds stems from the inability of classical ontological models, specifically the set-theoretic representation of the hypergraph corresponding to the quantum observables' collections, to adhere to and explain the observed statistics.