Embedding Quantum Mechanics Into a Broader Noncontextual Theory: A Conciliatory Result

TL;DR

This paper improves the ESR model, embedding quantum mechanics into a noncontextual framework, and demonstrates how modified and standard Bell inequalities relate under different measurement considerations, offering a unified interpretative perspective.

Contribution

It presents an improved ESR model that reconciles quantum predictions with noncontextual theories and clarifies the conditions under which different Bell inequalities apply.

Findings

Modified BCHSH inequality for all prepared systems

Standard quantum predictions for detected systems

Standard BCHSH inequality at the microscopic level

Abstract

The extended semantic realism (ESR) model embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here an improved version of this model and show that it predicts that, whenever idealized measurements are performed, a modified Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality holds if one takes into account all individual systems that are prepared, standard quantum predictions hold if one considers only the individual systems that are detected, and a standard BCHSH inequality holds at a microscopic (purely theoretical) level. These results admit an intuitive explanation in terms of an unconventional kind of unfair sampling and constitute a first example of the unified perspective that can be attained by adopting the ESR model.