Nonlinear Bell inequality for macroscopic measurements

TL;DR

This paper introduces a nonlinear Bell inequality that macroscopic measurement agents with limited control can violate, demonstrating nonclassical correlations in large-scale systems despite noise and classical expectations.

Contribution

The authors derive a Bell inequality applicable to macroscopic measurements that restricted agents can violate, even with noise scaling with system size.

Findings

Agents with limited control can violate the inequality.

Violations are feasible in various physical systems.

The inequality certifies nonclassicality without disproving local hidden variables.

Abstract

The correspondence principle suggests that quantum systems grow classical when large. Classical systems cannot violate Bell inequalities. Yet agents given substantial control can violate Bell inequalities proven for large-scale systems. We consider agents who have little control, implementing only general operations suited to macroscopic experimentalists: preparing small-scale entanglement and measuring macroscopic properties while suffering from noise. That experimentalists so restricted can violate a Bell inequality appears unlikely, in light of earlier literature. Yet we prove a Bell inequality that such an agent can violate, even if experimental errors have variances that scale as the system size. A violation implies nonclassicality, given limitations on particles' interactions. A product of singlets violates the inequality; experimental tests are feasible for photons, solid-state systems, atoms, and trapped ions. Consistently with known results, violations of our Bell inequality cannot disprove local hidden-variables theories. By rejecting the disproof goal, we show, one can certify nonclassical correlations under reasonable experimental assumptions.