Automated generation of photonic circuits for Bell tests with homodyne measurements

Nonlocal quantum realizations, certified by the violation of a Bell inequality, are core resources for device-independent quantum information processing. Although proof-of-principle experiments demonstrating device-independent quantum information processing have already been reported, identifying physical platforms that are realistically closer to practical, viable devices remains a significant challenge. In this work, we present an automated framework for designing photonic implementations of nonlocal realizations using homodyne detections and quantum state heralding. Combining deep reinforcement learning and efficient simulations of quantum optical processes, our method generates photonic circuits that achieve significant violations of the Clauser-Horne-Shimony-Holt inequality. In particular, we find an experimental setup, robust to losses, that yields a CHSH violation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>2.068</mml:mn> </mml:math> with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>3.9</mml:mn> </mml:math> dB and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0.008</mml:mn> </mml:math> dB squeezed light sources and two beam splitters.