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The origin of non-locality in Aspect-type experiments.

Werner A. Hofer

Published Sep 30, 2011• 0 citations
OpenAlex

Abstract

So far no mechanism is known, which could connect the two measurements in an Aspect-type experiment. Here, we suggest such a mechanism, based on the phase of a photon’s field during propagation. We show that two polarization measurements are correlated, even if no signal passes from one point of measurement to the other. The non-local connection of a photon pair is the result of its origin at a common source, where the two fields acquire a well defined phase difference. Therefore, it is not actually a non-local effect in any conventional sense. We expect that the model and the detailed analysis it allows will have a major impact on quantum cryptography and quantum computation.

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So far no mechanism is known, which could connect the two measurements in an Aspect-type experiment. Here, we suggest such a mechanism, based on the phase of a photon’s field during propagation. We show that two polarization measurements are correlated, even if no signal passes from one point of measurement to the other. The non-local connection of a photon pair is the result of its origin at a common source, where the two fields acquire a well defined phase difference. Therefore, it is not actually a non-local effect in any conventional sense. We expect that the model and the detailed analysis it allows will have a major impact on quantum cryptography and quantum computation.
So far no mechanism is known, which could connect the two measurements in an Aspect-type experiment. Here, we suggest such a mechanism, based on the phase of a photon’s field during propagation. We show that two polarization measurements are correlated, even if no signal passes from one point of measurement to the other. The non-local connection of a photon pair is the result of its origin at a common source, where the two fields acquire a well defined phase difference. Therefore, it is not actually a non-local effect in any conventional sense. We expect that the model and the detailed analysis it allows will have a major impact on quantum cryptography and quantum computation.
So far no mechanism is known, which could connect the two measurements in a Bell-type experiment with a speed beyond the speed of light, commonly considered the ultimate limit of propagation of any field-like interaction. Here, we suggest such a mechanism, based on the phase of a photon field during its propagation. We show that two measurements, corresponding to two independent rotations of the fields, are connected, even if no signal passes from one point of measurement to the other. The non-local connection of a photon pair is the result of its origin at a common source, where the two fields acquire a well defined phase difference. Therefore, it is not actually a non-local effect in any conventional sense.
Conventionally, one interprets the correlations observed in Einstein-Podolsky-Rosen experiments by Bell's inequalities and quantum nonlocality. We show, in this paper, that identical correlations arise, if the phase relations of electromagnetic fields are considered. In particular, we proceed from an analysis of a one-photon model. The correlation probability in this case contains a phase relation cos(b - a) between the two settings. In the two photon model the phases of the photon's electromagnetic fields are related at the origin. It is shown that this relation can be translated into a linearity requirement for electromagnetic fields between the two polarizers. Along these lines we compute the correlation integral with an expression conserving linearity. This expression, as shown, correctly describes the measured values. It seems thus that quantum nonlocality can be seen as a combination of boundary conditions on possible electromagnetic fields between the polarizers and a relation of the electromagnetic fields of the two photons via a phase. We expect the same feature to arise in every experiment, where joint probabilities of separate polarization measurements are determined.
The conventional interpretation of EPR-type experiments is based on Bell's inequalities and quantum nonlocality. In contrast, the model presented is strictly local. It is based on the analysis of consecutive polarization measurements. We show that the mathematical representation of these experiments contains a phase relation cos(b - a), connecting the two separate events conceptually. This feature of consecutive measurements, related to the phase of the photon's electromagnetic field, is at the bottom of the commonly assumed quantum nonlocality. We expect it to arise in every experiment, where joint probabilities of polarization measurements are determined.
Non-locality is one of the most characteristic trait of Quantum Mechanics, and it is linked to the conceptually counter-intuitive ability of some objects (when adequately prepared) to instantaneously know about each other’s state, no matter how much space-separated they are. At the development stage of Quantum Mechanics, non-locality had been an argument of intense debate among scientists due to its consequences that seemed to contradict physicists common sense. The scientific debate on the argument faced a turning point with the publication in 1964 of the landmark paper by J. S. Bell On the Einstein-Podolsky-Rosen Paradox, which ended the discussion whether or not non-locality was a true aspect of physical reality, raising it to one of the fundamental aspect of our comprehension of the physical world. The scientific interest for non-locality has recently substantially increased due to its striking applications in Quantum Information Theory. The major innovative traits of Quantum Information Theory, compared to Classical Information Theory, arise in fact from the usage of non-locality as a resource for information manipulation and transmission. The aim of this thesis is to investigate experimentally the non-local properties of a quantum system. This work is one of the first to prove that it is possible to share the non-local correlations of a two-photon entangled singlet state among three observers. The sharing of non-local correlations was possible through the employment of a weak measurement scheme, used to entangle the polarization degree of freedom of photons with a path degree of freedom used as ancilla for the weak measurement. In this thesis we briefly review all the theoretical tools necessary to understand the work (Quantum Mechanics, Optics, Quantum Optics) and we discuss in depth all the aspects of our work. We demonstrate theoretically how non-locality sharing is achievable, showing that it is possible to simultaneously violate two CHSH inequalities among three observers sharing a two-photon singlet state. We describe precisely our setup and its implementation. We finally present the obtained results, which confirm our theoretical model and expectations. The achievement of double violation and the realization of a simple weak measurement scheme may have important applications for Quantum Random Number Generation or for Quantum Key Distribution exploiting weak measurements.
Since John Bell has established his famous inequality and several independent experiments have confirmed the distinct polarization correlation of entangled photons predicted by quantum mechanics it is evident that quantum mechanics cannot be explained by local realistic theories. Actually, the observed polarization correlation can be deduced from wave optical considerations. The correlation has its origin in the phase coupling of the two circularly polarized wave packets leaving the photon source simultaneously. The experimental results violate Bell's inequality although no non-local interactions have to be assumed. In consequence the principle of locality remains valid in the scope of quantum mechanics. However, the principle of realism has to be replaced by the less stringent principle of contextuality.