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Automated Bell Inequality Violation using Uncalibrated Fiber Squeezing Polarization Controllers

Evan Dowling, Mark B. Morris, Gerald Baumgartner, Rajarshi Roy, Thomas E. Murphy

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We experimentally report on a real-time self-guided method to search for maximal CHSH violations between two observers sharing polarization entangled photon pairs using uncalibrated piezoelectric fiber squeezers as polarization controllers.
DOI
10.1364/cleo_fs.2023.fm1a.2

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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.
Abstract In addition to Bell's original inequality, John Clauser, Michael Horne, Abner Shimony, and Richard Holt (CHSH) developed a special form of Bell's inequality which gives classical limits to the expected correlation between two particles. We present a theoretical demonstration of the maximum value for violation of CHSH inequality, S = 2 2\sqrt{2}2​ , for the pure entangled quantum state. Using the spontaneous four‐wave mixing process, we generate polarization‐entangled photon pairs in a highly nonlinear fiber (HNLF) loop, for experimental verification. Using a nonentangled quantum state, we show theoretically that the violation of CHSH inequality is only a property of entangled states. We also show the theoretical solution of violation of the CHSH inequality for a general Greenberger–Horne–Zeilinger state and for an arbitrary state of two particles. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2454–2461, 2012; View this article online at wileyonlinelibrary. com. DOI 10.1002/mop.27127
Linearly polarized projections are the tacit means for performing Clauser-Horne-Shimony-Holt (CHSH) Bell-inequality tests using polarization-entangled photon pairs. The inequality is valid for all states on the Poincaré-Bloch sphere, but few laboratory studies have investigated violations with the full sphere. In this article, we explore the experimental verifications of the predicted violations of the CHSH inequality with Bell and non-Bell states with same and different linear and elliptically polarized basis states for each photon. We find that Bell states violate CHSH when using the same basis for both photons, regardless of their ellipticity, whereas they show no violations for photon projections in different bases. We found non-Bell maximally-entangled states for which the converse is true.