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.
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.
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.
As discussed below, Bell's inequalities and experimental results rule out commutative hidden variable models as a basis for Bell correlations, but not necessarily non-commutative probability models. A local probability model is constructed for Bell correlations based on non-commutative operations involving polarizers. As in the entanglement model, the Bell correlation is obtained from a probability calculus without explicit use of deterministic hidden variables. The probability calculus used is associated with chaotic light. Joint wave intensity correlations at spatially separated polarization analyzers are computed using common information originating at the source. When interpreted as photon count rates, these yield quantum mechanical joint probabilities after the contribution of indeterminate numbers of photon pairs greater than one is subtracted out. The formalism appears to give a local account of Bell correlations.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation.
Entangled photons leaving parametric down-conversion sources exhibit a pronounced polarization correlation. The data violate Bell's inequality thus proving that local realistic theories cannot explain the correlation results. Therefore many physicists are convinced that the correlation can only be brought about by non-local interactions. Some of them even assume that instantaneous influences at a distance are at work. Actually, assuming a strict phase correlation of the photons at the source the observed polarization correlation can be deduced from wave optical considerations. The correlation has its origin in the phase coupling of circularly polarized wave packets leaving the fluorescence photon source simultaneously. The enlargement of the distances between photon source and observers does not alter the correlation if the polarization status of the wave packets accompanying the photons is not changed on their way from the source to the observers. At least with respect to the polarization correlation of entangled photons the principle of locality remains valid.
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.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation. In particular, within the framework of a standard Bell experiment, i.e., a Bell inequality test that is directly performed on a single copy of a quantum state r, we have derived two algorithms to determine, respectively, a lower bound and an upper bound on the strength of correlations that r can offer for any given Bell inequality. Both of these algorithms make use convex optimization techniques in the form of a semidefinite program. By examples, we show that these algorithms can often be used in tandem, in conjunction with convexity arguments, to determine if a quantum state can offer nonclassical correlations and hence violates a given Bell inequality. On the other hand, since a standard Bell experiment typically involves measurements over many copies of the quantum systems, we have also investigated the possibility of enhancing the strength of nonclassical correlation by, instead, performing collective measurements on multiple copies of the quantum systems. Our findings show that even without postselection, such joint measurements may also lead to stronger nonclassical correlations, and hence a better Bell inequality violation. Meanwhile, previous studies have indicated that entangled state admitting locally causal models may still lead to observable nonclassical correlations if, prior to a standard Bell experiment, the state is subjected to some appropriate local preprocessing. This phenomenon of hidden nonlocality was discovered more than a decade ago, but to date, it is still not known if all entangled states can demonstrate nonclassical correlations through these more sophisticated Bell experiments. A key result in this thesis then consists of showing that for all bipartite entangled states, observable nonclassical correlations, in the form of a Bell-CHSH inequality violation, can indeed be derived if we allow both local preprocessing and the usage of shared ancillary state which by itself does not violate the Bell-CHSH inequality. This establishes a kind of equivalence between bipartite entanglement and states that cannot be simulated by classical correlations. In summary, for a standard Bell experiment where no local preprocessing on a quantum state r is allowed, we have provided two algorithms that can be used in tandem to determine if r can be simulated by a locally causal theory, whereas in the scenario where local preprocessing is allowed, we have demonstrated that bipartite entangled states are precisely those which cannot always be simulated classically.