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A Novel Method for Identifying Entangled Linearly–Elliptically Polarised Photon Pairs

Anton Lorenz Vrba

Published May 16, 2025• 0 citations
Publisher

Abstract

This work presents a method to establish entanglement of photon pairs in mixed (linear and elliptical) polarisation states. For such configurations, the standard Clauser–Horne–Shimony–Holt (CHSH) inequalities are projected to fail.Exploiting trigonometrical symmetries, we define a geometric correlation parameter $S^\dagger$, inspired by CHSH-type methods but algebraically distinct, which maintains maximal violation at $\sqrt{2}$ for all elliptical polarisation distortions induced by quarter-wave plates, and remains invariant across all four Bell states—$\ket{\psi^\pm}$ and $\ket{\phi^\pm}$. This result contrasts sharply with local hidden variable (LHV) models, which remain bounded by $S^\dagger \leq 1.5$ under the same conditions. Numerical simulations confirm that the proposed test functions as a robust entanglement witness; experimental verification is now essential.

DOI
10.31219/osf.io/pe4n2_v1

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This work presents a method to establish entanglement of photon pairs in mixed (linear and elliptical) polarisation states. For such configurations, the standard Clauser–Horne–Shimony–Holt (CHSH) inequalities are projected to fail.Exploiting trigonometrical symmetries, we define a geometric correlation parameter S†S^\daggerS†, inspired by CHSH-type methods but algebraically distinct, which maintains maximal violation at 2\sqrt{2}2​ for all elliptical polarisation distortions induced by quarter-wave plates, and remains invariant across all four Bell states—∣ψ±⟩\ket{\psi^\pm}∣ψ±⟩ and ∣ϕ±⟩\ket{\phi^\pm}∣ϕ±⟩. This result contrasts sharply with local hidden variable (LHV) models, which remain bounded by S†≤1.5S^\dagger \leq 1.5S†≤1.5 under the same conditions. Numerical simulations confirm that the proposed test functions as a robust entanglement witness; experimental verification is now essential.
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.
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.
Entanglement, describing the inseparability of a quantum multiparty system, is one of the most intriguing features of quantum mechanics. Violation of Bell inequality, for ruling out the possibility of local hidden variable theories, is commonly used as a strong witness for quantum entanglement. In previous Bell test experiments with photonic entanglement based on two-photon coincidence measurement, the photon temporal wave packets are absorbed completely by the detectors. That is, the photon coherence time is much shorter than the detection time window. Here we demonstrate generation of frequency-bin entangled narrowband biphotons, and for the first time, test the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality |S|<= 2 for their nonlocal temporal correlations with time-resolved detection. We obtain a maximum |S| value of 2.52+/-0.48 that violates the CHSH inequality. Our result will have applications in quantum information processing involving time-frequency entanglement.
It is well known that observing nonlocal correlations allows us to draw conclusions about the quantum systems under consideration. In some cases this yields a characterisation which is essentially complete, a phenomenon known as self-testing. Self-testing becomes particularly interesting if we can make the statement robust, so that it can be applied to a real experimental setup. For the simplest self-testing scenarios the most robust bounds come from the method based on operator inequalities. In this work we elaborate on this idea and apply it to the family of tilted Clauser-Horne-Shimony-Holt (CHSH) inequalities. These inequalities are maximally violated by partially entangled two-qubit states and our goal is to estimate the quality of the state based only on the observed violation. For these inequalities we have reached a candidate bound and while we have not been able to prove it analytically, we have gathered convincing numerical evidence that it holds. Our final contribution is a proof that in the usual formulation, the CHSH inequality only becomes a self-test when the violation exceeds a certain threshold. This shows that self-testing scenarios fall into two distinct classes depending on whether they exhibit such a threshold or not.
The Clauser-Horne-Shimony-Holt inequality (CHSH) is one of the most popular and well-studied witnesses of Bell's theorem, separating classical from quantum correlations. In this work, for every $d\ensuremath{\ge}2$, we present a generalization of the CHSH inequality with the property that maximal violation is achieved uniquely by the maximally entangled state of local dimension ddd. This provides an avenue for device-independent certification of maximally entangled states of arbitrary local dimension.
Entanglement swapping forms a key concept in the realization of scalable quantum networks and large-scale quantum communication. For the practical implementation of entanglement swapping, completely autonomous entanglement sources and a joint Bell-state measurement (BSM) between two independent photons are essential. Here, we experimentally demonstrate entanglement swapping between two independent polarization-entangled photon-pair sources obtained via spontaneous four-wave mixing (SFWM) in a Doppler-broadened atomic ensemble of 87 R b atoms. From the joint BSM, we estimate the S parameter in the Clauser–Horne–Shimony–Holt (CHSH) form of Bell’s inequality and confirm the violation of the Bell–CHSH inequality by S = 2.32 ± 0.07 with 4.5 standard deviations. We believe that this work is an important step toward realizing practical scalable quantum networks.