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arXiv:1908.06196

Bell correlations from previously entangled states of light

Louis Sica

Published Aug 16, 2019• 0 citations
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Abstract

Based on the Bell theorem and the resulting interpretation of the violation of Bell inequalities by experimental data, it has been believed that a theoretical computation of Bell correlations requires explicit use of the entanglement formalism. Physically this implies a permanent superposition of light waves in spite of the physical separation that occurs in the course of their propagation to spatially separated detectors. Nevertheless, in the present model, Bell correlations are calculated using explicitly separated waves with photon occurrence probabilities given by wave intensities based on nonlinear optics and quantum electrodynamics. The non-locality implied in the conventional calculation is thereby eliminated, but interference effects between photon excited waves and vacuum waves are assumed, as specified to be necessary in the design of Bell-experiment sources.

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Based on the Bell theorem and the resulting interpretation of the violation of Bell inequalities by experimental data, it has been believed that a theoretical computation of Bell correlations requires explicit use of the entanglement formalism. Physically this implies a permanent superposition of light waves in spite of the physical separation that occurs in the course of their propagation to spatially separated detectors. Nevertheless, in the present model, Bell correlations are calculated using explicitly separated waves with photon occurrence probabilities given by wave intensities based on nonlinear optics and quantum electrodynamics. The non-locality implied in the conventional calculation is thereby eliminated, but interference effects between photon excited waves and vacuum waves are assumed, as specified to be necessary in the design of Bell-experiment sources.
It has long been assumed that a theoretical computation of the Bell correlation necessitates the explicit use of an entangled state, based on the Bell theorem. In the down-converter sources utilized in Bell experiments, such a physical superposition of light waves occurs. Wave propagation to spatially distant detectors, on the other hand, eliminates this physical superposition. Local waves and the source boundary conditions of their previously entangled state must thus produce Bell correlations. Bell correlations are estimated in the present model using disentangled separated waves, nonlinear optics boundary conditions, and quantum electrodynamics features of single-photon and vacuum states. Based on the fact that the possibility of interference was found to be necessary by the designers of Bell-experiment sources, transient interference between photon-excited waves and photon-empty waves is assumed. Local random variables are used in this paradigm, but no underlying causality is specified. The current paper provides a calculation of the Bell correlation that begins with the principle that physically separated, non-superimposed, electromagnetic waves do not instantaneously influence each other.
Bell-state experiments with pairs of polarization-entangled photons are interpreted without any hinge on non-local mechanisms. The presented model rests on a careful analysis of published experimental findings. These foundations are implemented into a standard quantum mechanical treatment that obeys the purely local nature of each polarization preparation in the course of a measurement process. Polarization entanglement is ascribed to the generation of indiscernible photon pairs while undistorted propagation maintains this interrelation. Thus, the proposed approach assigns the essential characteristics of polarization entanglement to each constituent of an entangled pair. Accordingly, space-time separated polarization preparations lead to consistent probabilities of joint detection events. The obtained results agree with those of previous non-local models and thus reproduce the experimentally required violations of the Bell inequality. Since the presented approach lacks any non-local phenomenon, hidden variables are rendered superfluous, too.
Published experimental results and analytic developments indicate the possibility of achieving stronger correlations of physical events with independent photons rather than with entangled ones. The probability of coincident detections of quantum events should not be confused with the correlation of mixed states. The theoretical requirements for implementing the quantum nonlocality theory are not present in the experimental configurations purporting to prove Bohr’s or Bell’s nonlocality because of the quantum Rayleigh scattering of single photons. By means of a normalization factor corresponding to the total number of initiated events, the detection probabilities obtained experimentally are too small to enable any violation of a Bell inequality. Correlations between independent states of qubits can easily outperform those calculated with entangled photons. Additionally, the quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed
Published experimental results and analytic developments indicate the possibility of achieving stronger correlations of physical events with independent photons rather than with entangled ones. The probability of coincident detections of quantum events should not be confused with the correlation of mixed states. The theoretical requirements for implementing the quantum nonlocality theory are not present in the experimental configurations purporting to prove Bohr's or Bell's nonlocality because of the quantum Rayleigh scattering of single photons. By means of a normalization factor corresponding to the total number of initiated events, the detection probabilities obtained experimentally are too small to enable any violation of a Bell inequality. Correlations between independent states of qubits can easily outperform those calculated with entangled photons. Additionally, the quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed.
This paper aims to clarify the true physical relation of photon pairs and to falsify the "entanglement collapse" hypothesis that standard quantum mechanics imposes upon them. Bell experiments violating Bell's inequality only rule out "local independent hidden variables," and are not a sufficient condition for proving "superposition plus wave-function collapse." The physical definition of entanglement in standard quantum mechanics is: subsystems are strongly correlated, the system is inseparable, and the individual subsystem has no definite independent physical state; its mathematical expressions are the non-factorizability of pure-state wave functions and the non-convex-combination of mixed-state density matrices. The physical definition and mathematical expressions are fully aligned: the individual subsystem cannot be written as a separate expression and has no definite independent physical state. Operationally, it is also absolutely impossible to realize an individual measurement of the subsystem. However, in Bell experiments, photon pairs are separately and individually measured on spatially separated detectors, which directly falsifies the premise that "the photon pair is in an entangled state." Stripping away mysticism, the true relation of two photons is a linear equation with two unknowns (independent particles under an initial-state constraint); the three-photon logic (a linear equation with three unknowns) proves that after measuring one photon, the other two still have not collapsed into definite values and must still be measured individually to obtain their states—"wave-function collapse into a definite value" is purely fictitious in algebraic logic.
The locality condition of probabilities underpinning the derivation of Bell inequalities can be violated classically. The wave function collapse of an entangled state of single photons results in the factorization of quantum probabilities. It is possible to differentiate, locally, between ensemble probabilities of single detections with and without wave function collapse for the alleged quantum nonlocality. The theoretical concept of photonic quantum nonlocality cannot be implemented physically because of the quantum Rayleigh scattering of single photons. A distinction needs to be made between the correlation of individual, single measurements of pure states and the correlation of the measurement ensemble of the mixed states. The correlation operator of Pauli vector operators delivers the same probabilities of correlated detections of photons for both independent and multi-photon states as for ‘entangled’ states of photons. As single-photon sources are not needed, the design and implementation of quantum computing operations and other devices will be significantly streamlined.