Shifting the Quantum-Classical Boundary: Theory and Experiment for Statistically Classical Optical Fields

The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schr"odinger’s famous remark about it [Proc. Camb. Phil. Soc. 31, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than $\mathcal{B}=2.54$. This is many standard deviations outside the limit $\mathcal{B}=2$ established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit $\mathcal{B}=\mathrm{2.828...}$. These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.