Automated Bell inequality violation searches for estimating entanglement quality in fiber

In a future quantum network, two spatially separated individuals sharing a polarization entanglement source may need to assess the entanglement quality of the source without the presence of classical auxiliary signals. When the two are separated by a single-mode fiber, automated methods are necessary for the validation and estimation of polarization entanglement. We experimentally examine real-time iterative methods to search for maximal Bell violations, specifically the Clauser–Horne–Shimony–Holt (CHSH) inequality, between two observers sharing polarization entangled photons to evaluate the entanglement quality of the source. Our source allows us to tune the degree of entanglement of their shared photon pair by changing the temporal overlap of the two photons at an entangling 50/50 beam splitter so that we can compare the CHSH parameter these methods find to the theoretical values our source produces. The iterative methods used within our experiment are the Nelder–Mead optimization method, stochastic gradient descent, and Bayesian optimization. This is the first feedback experiment to study automated Bell violations in fiber and the first to compare all three of these iterative methods to one another in a quantum polarization control experiment. In our experiment, all methods are able to find Bell violations, but the Nelder–Mead method performed the best in terms of the speed and accuracy in finding the maximal violation.