Testing the Deviation of Single-Side Polarization State of Entangled Photons from Malus' Law: A Decisive Experimental Scheme Based on Coincidence Measurement
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.
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.
Conventional tests of Bell’s inequality rely on entangled photon pairs. Here, we replace entangled pairs with two independent photons of orthogonal polarization, and demonstrate that Bell’s inequality is still violated. Given the inherent local realism of independent photons, this experiment proves that Bell’s inequality cannot falsify the local realism of photons. We thus conjecture that the violation of Bell’s inequality by entangled photon pairs originates from their orthogonal polarizations, rather than the breakdown of local realism. To interpret this unexpected violation with independent photons, we further substitute the two photons with two monochromatic light beams, and calculate the transmittance correlation through polarizers via Malus’s law and Karl Pearson’s correlation formula. We show that this correlation also defies Bell’s inequality. Retracing the derivation of Bell’s inequality reveals its validity is restricted to binary events, which accounts for the observed violation with light beams. Finally, we propose a thought experiment involving gradual attenuation of light intensity down to the single-photon regime, and hypothesize that single-photon transmission through a polarizer does not constitute a binary event. This hypothesis provides a unified interpretation for both our experimental findings and all canonical Bell inequality tests reported to date.
We present an experimental study of polarization-entangled photon pairs, investigating the dependence of the measurement outcomes on different polarization rotation angles and the slow temporal fluctuations of the generated quantum state. Entangled photon pairs are produced and analyzed using single-photon detectors while systematically varying polarization settings on both sides. Bell tests yield an S parameter of approximately 2.52, confirming strong entanglement. The measured coincidence counts between identical measurement outcomes exhibit the expected sinusoidal dependence on the combined rotation angles, but systematic deviations appear as pronounced peaks and variations in certain configurations. Long-term monitoring over twenty minutes shows correlated fluctuations on both sides in individual detection outcomes of up to 25%, while the total photon flux remains constant, indicating that these deviations originate from slow intrinsic changes in the generated quantum state. These temporal fluctuations can reduce the effective time window over which optimal polarization and phase alignment is maintained, highlighting the importance of implementing real-time compensation or feedback mechanisms in experiments requiring high-fidelity entanglement over extended durations. Our results provide insight into the stability limits of entangled photon sources and underscore the importance of accounting for temporal fluctuations in precision entanglement experiments.
John Bell’s theorem of 1964 states that local elements of physical reality, existing independent of measurement, are inconsistent with the predictions of quantum mechanics (Bell, J. S. (1964), Physics (College. Park. Md). Specifically, correlations between measurement results from distant entangled systems would be smaller than predicted by quantum physics. This is expressed in Bell’s inequalities. Employing modifications of Bell’s inequalities, many experiments have been performed that convincingly support the quantum predictions. Yet, all experiments rely on assumptions, which provide loopholes for a local realist explanation of the measurement. Here we report an experiment with polarization-entangled photons that simultaneously closes the most significant of these loopholes. We use a highly efficient source of entangled photons, distributed these over a distance of 58.5 meters, and implemented rapid random setting generation and high-efficiency detection to observe a violation of a Bell inequality with high statistical significance. The merely statistical probability of our results to occur under local realism is less than 3.74×10-31, corresponding to an 11.5 standard deviation effect.
Abstract Quantum entanglement is an important action in quantum mechanics. Basically, quantum entanglement of correlated photon pairs can be produced by spontaneous down-conversion process inside the two birefringence crystals. This work aims to create a pair of photons, i.e. signal and idler, that are entangled and to assay the relation between these photons by using polarization-entangled photon pairs to demonstrate quantum non-locality by comparing with the Malus’s law. From the experiments, the coincidence counts as a function of relative angle (α - β) between transmission axis of the polarizer and analyzer were obtained and the polarization entanglement curve was demonstrated. This result corresponding with polarization entanglement prediction term of ½ cos2 (α - β) which confirmed the entanglement of photons.
This paper examines a local deterministic model of an experiment involving correlated photons. The experimental setup involves a source that emits two linearly polarized photons in each act, two two-channel analyzers, and detectors included in the coincidence scheme. The orientation angle of the photon polarization plane is a random variable with a uniform distribution, and it is the same for simultaneously emitted photons. The model presented here is a generalization of the “naive example of hidden variable theory” described in A. Aspect's article ‘Bell's Theorem: The Naive View of an Experimentalist. In our model, the outcome of the photon interaction with the analyzer (hit in one of the two channels) is uniquely determined by the angle between the photon polarization plane and the analyzer axis and is described by a step function. The difference in our model is that the step function contains a large number of segments of different lengths. The location and lengths of the segments are set so that the probability of a photon hitting a specific channel of an ideal analyzer, determined by averaging the outcomes over small neighborhoods of angles, approaches the Malus law when the maximum length of a segment decreases. This ensures that the classical model is self-consistent. When ideal analyzers are used, the absolute value of the correlation coefficient of detector readings mainly does not exceed the values from Aspect's ‘naive example’. However, when analyzers with absorption are used, the calculated correlations for some orientations of the analyzers exceed the quantum mechanical values. Key words: linear polarization of photons, Malus law, entangled photons, correlations, hidden parameters.
Malus’s law and the correlations of Bell-type experiments yield the same curve, the squared cosine of the angular offset between two polarizers. We propose a reinterpretation of both phenomena through a single mechanism: the correlation of responses at two points a and b, in series for Malus on a single photon, in parallel for Bell on two identical photons. No other situation is analyzed. The proposed resolution is strictly local, and reassigns cos²(a−b), observed in both cases, as the universal angular ratio of photons. The two experiments thus bring this correlation to light not because paired or polarized photons carry it, but because they make an otherwise invisible correlation testable. Bell’s theorem does not apply to this proposal, because cos²(a−b) is no longer read as the statistics of the responses at a and at b taken separately, but as the statistics of the responses at a and b taken jointly, independently of every other point. In other words, the cos² distribution of responses around an angle a holds only in association with the considered response at a, and does not constrain what the individual statistics of the response at b must be when the response at a is unknown. The article concludes that a strictly local explanation of Bell is possible again, and offers a falsifiable prediction: if identity sharing exists, understanding what it consists of will make it possible to produce identical photons without a common source.