Context-invariant and local quasi hidden variable (qHV) modelling versus contextual and nonlocal HV modelling

TL;DR

This paper introduces a context-invariant quasi hidden variable model for quantum measurements, providing a new upper bound on Bell inequality violations and highlighting advantages over traditional contextual models.

Contribution

The paper presents a novel, context-invariant quasi hidden variable model that applies to all joint von Neumann measurements on D-dimensional systems, offering a new bound on Bell inequality violations.

Findings

Existence of a context-invariant qHV model for all joint von Neumann measurements.

Derived a new exact upper bound on Bell inequality violations.

For qubits, the bound matches the maximal violation of the Mermin-Klyshko inequality.

Abstract

For all the joint von Neumann measurements on a D-dimensional quantum system, we present the specific example of a context-invariant quasi hidden variable (qHV) model, proved in [Loubenets, J. Math. Phys. 56, 032201 (2015)] to exist for each Hilbert space. In this model, a quantum observable X is represented by a variety of random variables satisfying the functional condition required in quantum foundations but, in contrast to a contextual model, each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. This, in particular, implies the specific local qHV (LqHV) model for an N-qudit state and allows us to derive the new exact upper bound on the maximal violation of 2x...x2-setting Bell-type inequalities of any type (either on correlation functions or on joint probabilities) under N-partite joint von Neumann measurements on an N-qudit state. For d=2, this new upper bound coincides with the maximal violation by an N-qubit state of the Mermin-Klyshko inequality. Based on our results, we discuss the conceptual and mathematical advantages of context-invariant and local qHV modelling.