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Journal of the Optical Society of America B

Variable Bell states in a polarization-entangled photon source

Shruti Sundar, M. V. Jabir, Daniel Razansky

Published Jun 13, 2025• 1 citation

Abstract

Bell states are fundamental resources in quantum optics, underpinning a range of applications in quantum computation and communication. However, many experimental sources focus on generating a single Bell state, limiting their utility for protocols that require the full set of maximally entangled states. In this work, we present a polarization-entangled photon-pair source based on spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate crystal integrated into a Sagnac loop interferometer. Our source initially generates one Bell state, which is then transformed into the complete set of Bell states through the application of phase and bit flips using phase plates. We characterize the entanglement quality of all generated states via two-photon interference measurements, quantum state tomography, and evaluation of the Bell parameter. Our results show spectral brightness of 0.15 kHz/mW/nm with interference visibilities of ∼98% (H/V basis) and ∼96% (A/D basis) and state fidelity of ∼0.97 across all Bell states, with all states demonstrating a clear violation of the Clauser–Horne–Shimony–Holt inequality (S≥2.6). This approach offers a practical solution for obtaining all four Bell states with high efficiency from a single source, which could facilitate more versatile implementations in quantum information processing.

DOI: 10.1364/josab.560031

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Sources of entangled photon pairs are a key component in both fundamental tests of quantum theory and practical applications such as quantum key distribution and quantum computing. In this work, we describe and characterize a source of polarization entangled photon pairs based on two spontaneous parametric down-conversion crystals in a Sagnac interferometer. Our source is compact and produces high-quality entangled states in a very flexible manner. The wavelengths of the photon pairs (around 810 and 1550 nm), the phase between orthogonal components of the entangled state, and the tangle of the state are all independently adjustable. In addition to presenting basic characterization data, we present experimental violations of Clauser-Horne-Shimony-Holt and Leggett inequalities, as well as an instance of the ``beautiful'' Bell inequality, which has not previously been tested experimentally.

We demonstrate pulsed operation of a bidirectionally pumped polarization Sagnac interferometric down-conversion source and its generation of narrow-band, high-visibility polarization-entangled photons. Driven by a narrow-band, mode-locked pump at 390.35 nm, the phase-stable Sagnac source with a type-II phase-matched periodically poled

{\text{KTiOPO}}_{4}

crystal is capable of producing 0.01 entangled pair per pulse in a 0.15-nm bandwidth centered at 780.7 nm with 1 mW of average pump power at a repetition rate of 31.1 MHz. We have achieved a mean photon-pair generation rate of as high as 0.7 pair per pulse, at which multipair events dominate and significantly reduce the two-photon quantum-interference visibility. For low generation probability $\ensuremath{\alpha}$, the reduced visibility $V=1\ensuremath{-}\ensuremath{\alpha}$ is independent of the throughput efficiency and of the polarization analysis basis, which can be utilized to yield an accurate estimate of the generation rate $\ensuremath{\alpha}$. At low $\ensuremath{\alpha}$ we have characterized the source entanglement quality in three different ways: average quantum-interference visibility of 99%, the Clauser-Horne-Shimony-Holt

S

parameter of $2.739\ifmmode\pm\else\textpm\fi{}0.119$, and quantum state tomography with 98.85% singlet-state fidelity. The narrow-band pulsed Sagnac source of entangled photons is suitable for use in quantum information processing applications such as free-space quantum key distribution.

We report a source of polarization-entangled photon pairs in the 1550-nm telecommunication band, which is based on non-collinear spontaneous parametric down-conversion in a periodically poled lithium niobate crystal pumped by picosecond pulses. This source is realized utilizing a polarization-based Sagnac interferometer employing a type-0 non-collinear quasi-phase-matching configuration. Polarization entanglement is verified through measurement of the polarization-correlation interference fringes with visibility >96% and by testing the experimental violation of the Clauser-Horne-Shimony-Holt (CHSH) form of Bell's inequality. The CHSH-Bell parameter S is found to be 2.72 ± 0.04, with 18 standard deviations from the statistical uncertainty.

We present a simple but highly efficient source of polarization-entangled photons based on spontaneous parametric down-conversion (SPDC) in bulk periodically poled potassium titanyl phosphate crystals (PPKTP) pumped by a 405 nm laser diode. Utilizing one of the highest available nonlinear coefficients in a non-degenerate, collinear type-0 phase-matching configuration, we generate polarization entanglement via the crossed-crystal scheme and detect 0.64 million photon pair events/s/mW, while maintaining an overlap fidelity with the ideal Bell state of 0.98 at a pump power of 0.025 mW.

We present a simple but highly efficient source of polarization-entangled photons based on spontaneous parametric down-conversion (SPDC) in bulk periodically poled potassium titanyl phosphate crystals (PPKTP) pumped by a 405 nm laser diode. Utilizing one of the highest available nonlinear coefficients in a non-degenerate, collinear type-0 phase-matching configuration, we generate polarization entanglement via the crossed-crystal scheme and detect 0.64 million photon pair events/s/mW, while maintaining an overlap fidelity with the ideal Bell state of 0.98 at a pump power of 0.025 mW.