Optimal conditions for Bell test using spontaneous parametric down-conversion sources

TL;DR

This paper investigates the optimal conditions for Bell tests using SPDC sources, showing that a higher average photon number enhances CHSH violation and proposing a method to estimate ideal Bell values from lossy data.

Contribution

It combines theoretical analysis and experimental validation to identify optimal SPDC parameters for Bell tests and introduces a novel method to estimate ideal Bell violations from imperfect data.

Findings

Optimal photon number for maximum CHSH violation is around 0.5.

Experimental results align with theoretical predictions despite detection inefficiencies.

A new method estimates ideal Bell violation values from lossy experimental data.

Abstract

We theoretically and experimentally investigate the optimal conditions for the Bell experiment using spontaneous parametric down conversion (SPDC) sources. In theory, we show that relatively large average photon number (typically $\sim$0.5) is desirable to observe the maximum violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. In experiment, we perform the Bell experiment without postselection using polarization entangled photon pairs at 1550 nm telecommunication wavelength generated from SPDC sources. While the violation of the CHSH inequality is not directly observed due to the overall detection efficiencies of our system, the experimental values agree well with those obtained by the theory with experimental imperfections. Furthermore, in the range of the small average photon numbers ($\leq0.1$), we propose and demonstrate a method to estimate the ideal CHSH value intrinsically contained in the tested state from the lossy experimental data without assuming the input quantum state.