Quantum-Like Correlations from Local Hidden-Variable Theories Under Conservation Law

Abstract

The precision with which we can measure operators that do not commute with conserved quantities is limited by the need to preserve the associated global symmetries. We show how to construct a local hidden-variable model that violates Bell inequalities by interpreting this measurement error as altering the measure space of the hidden variables. This provides a physically-motivated example of a supermeasured model, where the statistical independence assumption used to form Bell inequalities is violated without there being a causal dependence of the measurement settings on the hidden variables (superdeterminism) or a causal dependence of the hidden variables on the measurement settings (retrocausality). The model also gives subtly different predictions to quantum mechanics, that could be tested experimentally.

Figures (1)

• Figure 1: Bell test correlation response functions predicted by quantum mechanics ($E^{qm}$) and hidden-variable models considering conservation of angular momentum ($E_L^{hv}$) with various values of $\Delta L$ for the Bell singlet $|\psi^-\rangle$ and triplet $|\psi^+\rangle$.