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Journal of the Optical Society of America B

Phase-shifted Bell states

J. J. Joshua Davis, Carey L. Jackman, R. Leonhardt, Paul J. Werbos, Maarten D. Hoogerland

Published Apr 9, 2025• 4 citations
Publisher

Abstract

Inspired by previous studies and pioneers of the field, we present new results on an extensive Einstein, Podolsky, and Rosen (EPR)–Bell experiment using photons generated by parametric down-conversion, where one of the photons is deliberately phase-shifted. Our experiments show some surprising results for particular angles of this phase shift, where, for some states, the Clauser, Horne, Shimony, and Holt inequality shows no violations, requiring us to review our understanding of “entangled” states vis-à-vis the correlations obtained via experimental coincidence counts in agreement with quantum mechanics theoretical predictions. We give some possible explanations about the correlated states that show no violations of these inequalities.

DOI
10.1364/josab.552007

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Inspired by previous studies and pioneers of the field, we present new results on an extensive Einstein, Podolsky, and Rosen (EPR)–Bell experiment using photons generated by parametric down-conversion, where one of the photons is deliberately phase-shifted. Our experiments show some surprising results for particular angles of this phase shift, where, for some states, the Clauser, Horne, Shimony, and Holt inequality shows no violations, requiring us to review our understanding of “entangled” states vis-à-vis the correlations obtained via experimental coincidence counts in agreement with quantum mechanics theoretical predictions. We give some possible explanations about the correlated states that show no violations of these inequalities.
This paper conveys briefly and concisely what could be the implications of the Einstein-Bohr debate when we consider the results of Phase-Shifted EPR-Bell states from a study conducted in Maarten Hoogerland’s Lab in the Dodd-Walls Centre for Photonics and Quantum Technologies, University of Auckland, New Zealand (2018-2024). The results of this study were presented at the first Biological Physics and Meaning Mini Conference on ‘QUANTUM MECHANICS, THE MEASUREMENT PROBLEM AND HUMAN CONSCIOUSNESS’ (Feb. 2024). Here, I also examine the nature of correlated pairs of photons produced by Spontaneous Parametric Down Conversion (SPDC) Type II, when the photon of one path is altered with a Quarter Wave Plate (QWP), shifting the polarization from linear to elliptical or circular. As stated in the above mentioned study, surprisingly, some of these Phase Shifted Bell states (correlated pairs) produce no violation of the Clauser, Horne, Shimony and Holt (CHSH) inequality, raising yet again a question mark on the meaning of ‘entanglement’ when understood as ‘spooky action at a distance’, in the context of the formalism of Quantum Mechanics and the different associated interpretations. If ‘spooky action at a distance’ is ruled out from physical systems and we consider new more general stochastic laws, then we open the way for a more interesting future physics on the side of Einstein and realism that, under some regimes, may manifest as nonlocality in terms of information structures. Perhaps, religious, spiritual and mystical experience (RSME) may have a place in physics and the sciences in general, as experienced information and meaning within physical restrictions in a classically consciously experienced lived life in spacetime.
The aim of this paper is to attract the attention of experimenters to the original Bell (OB) inequality that was shadowed by the common consideration of the Clauser-Horne-Shimony-Holt (CHSH) inequality. There are two reasons to test the OB inequality and not the CHSH inequality. First of all, the OB inequality is a straightforward consequence to the Einstein-Podolsky-Rosen (EPR) argumentation. In addition, only this inequality is directly related to the EPR-Bohr debate. The second distinguishing feature of the OB inequality was emphasized by Itamar Pitowsky. He pointed out that the OB inequality provides a higher degree of violations of classicality than the CHSH inequality. For the CHSH inequality, the fraction of the quantum (Tsirelson) bound Q CHSH = 2 2 to the classical bound C CHSH = 2 , i.e., F CHSH = Q CHSH C CHSH = 2 is less than the fraction of the quantum bound for the OB inequality Q OB = 3 2 to the classical bound C OB = 1 , i.e., F OB = Q OB C OB = 3 2 . Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations. However, the last few years have been characterized by the amazing development of quantum technologies. Nowadays, there exist sources producing, with very high probability, the pairs of photons in the singlet state. Moreover, the efficiency of photon detectors was improved tremendously. In any event, one can start by proceeding with the fair sampling assumption. Another possibility is to use the scheme of the Hensen et al. experiment for entangled electrons. Here, the detection efficiency is very high.
Abstract This chapter presents a detailed discussion of Bell inequalities and their experimental tests. Starting from the Aharonov-Bohm version of the Einstein-Podolsky-Rosen (EPR) paradox, we review EPR’s criteria for realism and completeness and Bell’s locality condition, before deriving the Clauser-Horne-Shimony-Holt (CHSH) inequality. This is followed by an exposition on Bell’s original inequality and other Bell inequalities by Wigner, as well as Clauser and Horne. We then discuss the milestones in the experimental violation of Bell inequalities, from the experiment of Freedman and Clauser in the 1970s, to the efforts of Aspect et al. in the 1980s, the experiments by the teams of Zeilinger and Gisin in the 1990s, and culminating the loophole-free tests in 2015. Finally we turn to a brief discussion of the interpretations of quantum mechanics, focusing on contrasting the realist views held by, e.g., Einstein and Bell, and the informational views with proponents such as Brukner and Zeilinger
The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schrödinger's famous remark about it [Proc. Camb. Phil. Soc. 31, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than B=2.54{\cal B} = 2.54B=2.54. This is many standard deviations outside the limit B=2{\cal B} = 2B=2 established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit B=2.828...{\cal B} = 2.828...B=2.828.... These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.
In 1935, Einstein, Podolsky, and Rosen (EPR) argued that (then new) quantum mechanics was incomplete. At the heart of EPR’s paradox was the strange non-local nature of an entangled state which allowed EPR to simultaneously assign local values for position and momentum of a particle. In 1964, John Bell proposed an inequality (Bell’s inequality) that must be satisfied by any local realistic theory. The experimental confirmation of quantum physics, i.e., the experimental test of Bell’s inequality, required a pair of particles in an entangled state. The experiments first performed in the early 1970s, followed by a series of experiments until now, have confirmed the violation of Bell’s inequality, strongly implying that local realistic descriptions of nature are not consistent with experimental observations. The early simplistic view of entanglement has now been significantly expanded to include mixed states and multiple particles. Moreover, theoretical and experimental studies on the nature of entanglement have led to quantum information science where entanglement is an essential resource. In this article, we briefly review the early experiments on Bell’s inequality and experimental attempts to close “loopholes” as well as some key experiments on quantum information.