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Possible Vulnerability of Bell-Clauser-Horne-Shimony-Holt Tests used for Quantum Certification

F. De Zela

TL;DR

The paper investigates whether Bell-CHSH tests used for quantum certification can be fakely satisfied by classical hidden-variable descriptions. It introduces a local realist HV model with a non-factorable joint density $p_{AB}$, derived via Lebesgue decomposition, that reproduces quantum predictions for the singlet state, yielding $P^{HV}_{ψ−}(α,β|a,b)=1/4(1-αβ a·b)$ and $⟨AB⟩^{HV}_{ψ−}=-a·b$. This demonstrates that Bell-CHSH violations do not uniquely certify quantumness or entanglement, highlighting a vulnerability in quantum-certification schemes that rely solely on CHSH violations. The results emphasize the need for stronger, more robust certification criteria and careful interpretation of locality, factorization, and measurement-independence assumptions in device-independent protocols.

Abstract

A hidden variables (HVs) model is reported, which reproduces quantum predictions for Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) tests. The existence of such a model poses some limitations to quantum certifications that rely on Bell-CHSH inequality violations. The reported model does not prove wrong Bell's theorem. The latter assumes the factorability of the probability density $p_{AB}$, which rules the stochastic behavior of the HVs. The reported HVs model is based on an extended form of $p_{AB}$, which is suggested by Lebesgue's decomposition theorem for bounded functions. The considered $p_{AB}$ complies with locality and realism, and also with measurement independence, parameter independence and outcome independence.

Possible Vulnerability of Bell-Clauser-Horne-Shimony-Holt Tests used for Quantum Certification

TL;DR

The paper investigates whether Bell-CHSH tests used for quantum certification can be fakely satisfied by classical hidden-variable descriptions. It introduces a local realist HV model with a non-factorable joint density , derived via Lebesgue decomposition, that reproduces quantum predictions for the singlet state, yielding and . This demonstrates that Bell-CHSH violations do not uniquely certify quantumness or entanglement, highlighting a vulnerability in quantum-certification schemes that rely solely on CHSH violations. The results emphasize the need for stronger, more robust certification criteria and careful interpretation of locality, factorization, and measurement-independence assumptions in device-independent protocols.

Abstract

A hidden variables (HVs) model is reported, which reproduces quantum predictions for Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) tests. The existence of such a model poses some limitations to quantum certifications that rely on Bell-CHSH inequality violations. The reported model does not prove wrong Bell's theorem. The latter assumes the factorability of the probability density , which rules the stochastic behavior of the HVs. The reported HVs model is based on an extended form of , which is suggested by Lebesgue's decomposition theorem for bounded functions. The considered complies with locality and realism, and also with measurement independence, parameter independence and outcome independence.
Paper Structure (8 sections, 29 equations, 1 figure)

This paper contains 8 sections, 29 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Bell's model and the Bell-CHSH inequality
  3. Hidden variables model that violates the Bell-CHSH inequality
  4. Preliminary remarks
  5. Locality and non-locality: two properties that do not exclude each other
  6. Proposed local realist model outside of Bell's framework
  7. Comparison with other models that reproduce quantum predictions
  8. Closing remarks

Figures (1)

  • Figure 1: Bell-CHSH experiment: Entangled pairs of spin-1/2 particles are produced by a source. One particle is sent to site $A$ and the other to site $B$. On each site, SG-magnets have a binary outcome ($\pm 1$). Each magnet can be oriented along two directions, $\boldsymbol{\hat{a}}$, $\boldsymbol{\hat{a}'}$ at $A$, and $\boldsymbol{\hat{b}}$, $\boldsymbol{\hat{b}'}$ at $B$. The raw data of the experiment consist of simultaneous detections at $A$ and $B$.