When elliptically polarized maximally entangled states are considered, i.e., states having a non random phase factor between the two bipartite polarization components, the standard settings used for optimal violation of Bell inequalities are no longer adapted. One way to retrieve the maximal amount of violation is to compensate for this phase while keeping the standard Bell inequality analysis settings. We propose in this paper a general theoretical approach that allows determining and adjusting the phase of elliptically polarized maximally entangled states in order to optimize the violation of Bell inequalities. The formalism is also applied to several suggested experimental phase compensation schemes. In order to emphasize the simplicity and relevance of our approach, we also describe an experimental implementation using a standard Soleil-Babinet phase compensator. This device is employed to correct the phase that appears in the maximally entangled state generated from a type-II nonlinear photon-pair source after the photons are created and distributed over fiber channels.
When elliptically polarized maximally entangled states are considered, i.e., states having a non random phase factor between the two bipartite polarization components, the standard settings used for optimal violation of Bell inequalities are no longer adapted. One way to retrieve the maximal amount of violation is to compensate for this phase while keeping the standard Bell inequality analysis settings. We propose in this paper a general theoretical approach that allows determining and adjusting the phase of elliptically polarized maximally entangled states in order to optimize the violation of Bell inequalities. The formalism is also applied to several suggested experimental phase compensation schemes. In order to emphasize the simplicity and relevance of our approach, we also describe an experimental implementation using a standard Soleil-Babinet phase compensator. This device is employed to correct the phase that appears in the maximally entangled state generated from a type-II nonlinear photon-pair source after the photons are created and distributed over fiber channels.
We demonstrate high quality polarization entanglement at telecom wavelength, based on guided-wave technology. The fully fibered setup relies on a type-II periodically poled Lithium Niobate waveguide (PPLN/W) emitting pairs of cross-polarized photons (H,V) at 1310 nm. These photon pairs are sent onto a simple 50/50 fiber-optic coupler, leading to an entangled state of the form |Ψ>=(1/21/2)*(|Ha,Vb>+|Va,Hb>) in the coincidence basis, which is eventually distributed to "users" (a,b) through standard optical fibers. Along these distribution channels, the entangled state acquires an unknown phase between its two components leading to an "elliptically polarized" maximally entangled states |Ψ>=(1/21/2)*(| Ha,Vb>+eiφ|Va,Hb>), in which φ is a non random phase, and (a,b) represent the two channels at the output of the emitting source. For such a state, the usual settings used for optimal violation of the Bell inequality are no longer adapted. Thanks to the use of a phase compensator, namely a Soleil-Babinet birefringent system, we demonstrate experimentally that any phase can be compensated, leading to a maximal violation of the Bell inequality when the standard settings are used. Alternatively, we propose here a theoretical approach that allows, when applied to those particular states, determining the phase, and finding new analysis parameters towards optimizing the Bell inequality violation. After introducing our formalism in its generic form, we will show that it can be applied to several existing systems capable of either compensating or analyzing the phase.
Bell’s inequality plays an important role in quantum mechanics. Many experiments have been made to test the Bell’s inequality by using various bipartite entangled sources. However, the maximal violation of the Bell inequality (i.e., the Cirel’son’s limit) has not been reached yet, due to various practically-existing imperfections (e.g., entangled source is not the pure maximally-entangled state, and the measurement settings used are not the best ones). In this paper, we investigate experimentally an approach to enhance the violation degree of Bell’s inequality with the commercialized entangled photons by optimizing the measurement settings for the experimentally-reconstructed density matrix of the entangled photons. It is shown that the measurement setting related to the pure entangled state can not get maximally violation generally. However, upon the density matrix reconstructed by tomographic technique, optimal measurement settings can be found. With these optimal settings, we consequently found that the violation degree of the Bell’s inequality can be increased. This suggests a possible approach to optimize the test of Bell’s inequality.
Photon-based entanglement sources, crucial for obtaining entangled states, are typically generated via spontaneous parametric down-conversion. However, birefringence in nonlinear crystals causes spatial or temporal walk-off, reducing entangled photon quality. The theoretical analysis attributes birefringent walk-off to dispersive materials curbed by pre- and post-compensation. We experimentally validate this method, enhancing polarization-entangled photon quality. We measured the Bell state along with a violation of CHSH-Bell's inequality by ∼366 standard deviations (S = 2.623 ± 0.0017). Our approach, simple and stable, does not complicate setups. Its applicability extends to optimizing various entanglement source schemes, aiding optical quantum technologies such as computation, sensing, and communication.
Bell inequality experiments have demonstrated that quantum entanglement violates the predictions of local realism. However, all Bell experiments are based on joint measurements of two photons, and their analysis implicitly assumes that "the polarization state of a single photon is ideally linear." This paper proposes an experimental scheme to directly test this assumption: using type-II spontaneous parametric down-conversion (SPDC) to generate polarization-entangled photon pairs, employing fixed-angle measurement of the e-light channel as a coincidence gate to filter entangled photons in the o-light channel, then scanning the o-light analyzer angle with high precision to measure the coincidence count rate as a function of the analyzer angle, testing whether it strictly follows Malus' law I(\theta)=I_0\cos^2(\theta-\theta_0). If systematic deviation is observed in the curve, it would indicate the existence of asymmetric secondary polarization structures in the polarization state of entangled photons, providing an alternative explanatory pathway for Bell inequality violation distinct from nonlocality. This experiment employs a high-precision coincidence measurement scheme to ensure statistical significance and designs multiple control experiments to eliminate systematic errors. The experiment can be implemented in laboratories equipped with standard quantum optics equipment.
We use a tunable quantum interference in type-II parametric down-conversion to construct two-photon quantum states that exhibit less-than-maximal, and tunable, violations of Bell-type inequalities. These states, no longer singlet-state analogs, possess an interference term of controllable magnitude that we adjust by tuning the measurement bandwidth. We show violations of two Bell-type inequalities in polarization variables, one more general than the other. We use these tunable violations to probe the threshold degree of interference that must be present to generate a violation, using an appropriate quantitative figure of merit.
Bell's inequality violation experiments are becoming increasingly popular in the practical teaching of undergraduate and master's degree students. Bell's parameter S is obtained from 16 polarization correlation measurements performed on entangled photons pairs. We first report here a detailed analysis of the uncertainty u(S) of Bell's parameter taking into account coincidence count statistics and errors in polarizers' orientation. We show using both computational modeling and experimental measurement that the actual sequence of the polarizer settings has an unexpected and strong influence on the error budget. This result may also be relevant to measurements in other settings in which errors in parameters may have non-random effects in the measurement.