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On the Computer Simulation of the EPR-Bohm Experiment

David O. McGoveran, H. Pierre Noyes, M J Manthey

Published Dec 1, 1988• 0 citations
OpenAlex

Abstract

We argue that supraluminal correlation without supraluminal signaling is a necessary consequence of any finite and discrete model for physics.Every day, the commercial and military practice of using encrypted communication based on correlated, pseudo-random signals illustrates this possibility.All that is needed are two levels of computational complexity which preclude using"a smaller system to detect departures from "randomness" in the larger system.Hence, the experimental realizations of the EPR-Bohm experiment leave open the question of whether the world of experience is "random" or pseudo-random.The latter possibility could be demonstrated experimentally if a complexity parameter related to the arm length and switching time in an Aspect-type realization of the EPR-Bohm experiment is sufficiently small compared to the number of reliable total counts ..--. which can be obtained in practice.

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Communication loophole in a Bell-EPR-Bohm experiment: standard no-signaling may not always be enough to exclude local realism

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Assuming perfect detection efficiency, we present an (indeterministic) model for an EPR-Bohm experiment which reproduces the singlet correlations, without contradicting Bell's original locality condition. In this model we allow the probability distribution $ρ_λ$ of the state $λ$ at the source to depend parametrically on the orientation $ξ$ of one of the measuring devices: $ρ_λ(λ,ξ)$. In a Bell experiment, no-signaling between the source and each one of the devices would seem clearly sufficient to rule such an influence; however, not even schemes where the choice of observables takes place during the on-flight time of the particles can prevent, in some situations, a model of this type from violating the local bounds. In particular, a random shift $ρ_λ(λ,ξ_1) \rightarrow ρ_λ(λ,ξ_2) \rightarrow...\rightarrow ρ_λ(λ,ξ_n)$ allows the model to perform a "subensemble selection" for each of the terms involved in the inequality (analogous to what goes on with the efficiency loophole), whenever some correlation of those $ρ_λ$-shifts with the sequence of measurement choices is allowed. That correlation does not necessarily imply signaling during the photon on-flight time.

arXiv:1108.4823•Aug 24, 2011•0 citations

Bell's inequalities and EPR–Bohm correlations: working classical radiofrequency model

N. V. Evdokimov, Давид Николаевич Клышко, Владимир Павлович Комолов +1 more

A description is given of an electron model which makes it possible to simulate pair correlation of random dichotomous signals of the Einstein–Podolsky–Rosen (EPR) type in the Bohm variant. This model can be used to demonstrate that Bell's inequality is satisfied in classical physics. Some features of parametric rf oscillators are used in the model. An analysis of the operation of the model helps one to understand the difference between quantum and classical correlations in EPR experiments. A specific mechanism is suggested for 'nonlocal' control of EPR-type correlations between distant observers, which applies to classical and quantum models. A controlled correlation between two random telegraphic signals is ensured by transmission, to two observers, of a sequence of pulses with the same random phase. An elementary derivation of Bell's inequality is given and an analysis is made of the logic of the use of the popular term 'quantum nonlocality' employed usually in the description of the quantum variants of the investigated experiment.

Physics-Uspekhi•Jan 31, 1996•30 citations

EPR Paradox, Locality and Completeness of Quantum Theory

Marian Kupczyński, Guillaume Adenier, Andrei Yu. Khrennikov +3 more

The quantum theory (QT) and new stochastic approaches have no deterministic prediction for a single measurement or for a single time‐series of events observed for a trapped ion, electron or any other individual physical system. The predictions of QT being of probabilistic character apply to the statistical distribution of the results obtained in various experiments. The Copenhagen interpretation (CI) of QT acknowledged the abstract and statistical character of the predictions of QT but at the same time claimed that a state vector Ψ provided complete description of each individual physical system. The assigning the state vector to an individual physical system together with a postulate of its instantaneous reduction in the measurements was shown by Einstein Podolski and Rosen to lead to so called EPR paradox for the experiments with the entangled pairs of the particles. EPR concluded that a state vector could not provide a complete description of the individual systems and the question arose whether the probabilistic predictions of QT could be derived from some more fundamental spatio‐temporal deterministic description of the invisible sub‐phenomena by introduction of supplementary parameters. The experimental violation of the Bell inequalities in the spin polarization correlation experiments (SPCE) which were the implementations of Bohm and EPR gedanken experiments eliminated so called local and realistic models of the sub‐phenomena. Quite often the violation of these inequalities has been incorrectly interpreted as a proof of the completeness of QT or as the violation of the locality and causality in the micro‐world. The local and realistic models overlooked the fact that an experimental outcome is only the information about a particular system‐system or system‐instrument interaction. Namely the quantum phenomena are described in terms of the probabilities. It is well known that the probability distribution is not an attribute of a dice but it is a characteristic of a whole random experiment: “rolling a dice”. In this paper we will underline: that the quantum probabilities do not describe the lack of knowledge about the physical systems but the lack of knowledge about the experiments and therefore they are “contextual” and that the statistical long range correlations between two random variables X and Y are not a proof of any causal relation between these variables. Moreover any probabilistic model used to described a random experiment is consistent only with a specific protocol telling how the random experiment has to be performed. The probabilistic model used to prove Bell inequalities implied a protocol completely inappropriate and impossible to implement for SPCE . We conclude that the meaningful question about the predictable completeness of QT is still open and it should be answered by a careful and unconventional analysis of the experimental data. The correct understanding of statistical and contextual character of QT is essential for the research in the domain of quantum information and quantum computing.

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How Random Is Quantum Randomness? An Experimental Approach

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Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a necessary, but not sufficient "symptom" of "true randomness". We base our experimental approach on algorithmic information theory which provides characterizations of algorithmic random sequences in terms of the degrees of incompressibility of their finite prefixes. Algorithmic random sequences are incomputable, but the converse implication is false. We have performed tests of randomness on pseudo-random strings (finite sequences) of length $2^{32}$ generated with software (Mathematica, Maple), which are cyclic (so, strongly computable), the bits of $π$, which is computable, but not cyclic, and strings produced by quantum measurements (with the commercial device Quantis and by the Vienna IQOQI group). Our empirical tests indicate quantitative differences, some statistically significant, between computable and incomputable sources of "randomness".

arXiv:0912.4379•Dec 22, 2009•2 citations

The EPR correlations and the chameleon effect

Luigi Accardi, Massimo Regoli

We describe an experiment in which two non communicating computers, starting from a common input in the form of sequences of pseudo--random numbers in the interval $[0,2π]$, and computing deterministic $\{\pm 1\}$--valued functions, chosen at random and independently, produce sequences of numbers whose correlations coincide with the EPR correlations and therefore violate Bell's inequality. The experiment is the practical implementation of a mathematical model of a classical, deterministic system whose initial state is chosen at random from its state space, with a known initial probability distribution, and whose dynamics exhibits the chameleon effect described below. Such a system satisfies the constraints of pre--determination, locality, causality, local independent choices, singlet law and reproduces the EPR correlations.

arXiv:quant-ph/0110086•Oct 13, 2001•16 citations

Classical (Local and Contextual) Probability Model for Bohm–Bell Type Experiments: No-Signaling as Independence of Random Variables

Andrei Yu. Khrennikov, A. P. Alodjants

We start with a review on classical probability representations of quantum states and observables. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The main part of the paper is devoted to the conditional probability model with conditioning on the selection of the pairs of experimental settings. From the viewpoint of quantum foundations, this is a local contextual hidden-variables model. Following the recent works of Dzhafarov and collaborators, we apply our conditional probability approach to characterize (no-)signaling. Consideration of the Bohm–Bell experimental scheme in the presence of signaling is important for applications outside quantum mechanics, e.g., in psychology and social science. The main message of this paper (rooted to Ballentine) is that quantum probabilities and more generally probabilities related to the Bohm–Bell type experiments (not only in physics, but also in psychology, sociology, game theory, economics, and finances) can be classically represented as conditional probabilities.

arXiv:1812.10826•Entropy•Feb 8, 2019•56 citations
We argue that supraluminal correlation without supraluminal signaling is a necessary consequence of any finite and discrete model for physics.Every day, the commercial and military practice of using encrypted communication based on correlated, pseudo-random signals illustrates this possibility.All that is needed are two levels of computational complexity which preclude using"a smaller system to detect departures from "randomness" in the larger system.Hence, the experimental realizations of the EPR-Bohm experiment leave open the question of whether the world of experience is "random" or pseudo-random.The latter possibility could be demonstrated experimentally if a complexity parameter related to the arm length and switching time in an Aspect-type realization of the EPR-Bohm experiment is sufficiently small compared to the number of reliable total counts ..--. which can be obtained in practice.
Assuming perfect detection efficiency, we present an (indeterministic) model for an EPR-Bohm experiment which reproduces the singlet correlations, without contradicting Bell's original locality condition. In this model we allow the probability distribution ρλρ_λρλ​ of the state λλλ at the source to depend parametrically on the orientation ξξξ of one of the measuring devices: ρλ(λ,ξ)ρ_λ(λ,ξ)ρλ​(λ,ξ). In a Bell experiment, no-signaling between the source and each one of the devices would seem clearly sufficient to rule such an influence; however, not even schemes where the choice of observables takes place during the on-flight time of the particles can prevent, in some situations, a model of this type from violating the local bounds. In particular, a random shift ρλ(λ,ξ1)→ρλ(λ,ξ2)→...→ρλ(λ,ξn)ρ_λ(λ,ξ_1) \rightarrow ρ_λ(λ,ξ_2) \rightarrow...\rightarrow ρ_λ(λ,ξ_n)ρλ​(λ,ξ1​)→ρλ​(λ,ξ2​)→...→ρλ​(λ,ξn​) allows the model to perform a "subensemble selection" for each of the terms involved in the inequality (analogous to what goes on with the efficiency loophole), whenever some correlation of those ρλρ_λρλ​-shifts with the sequence of measurement choices is allowed. That correlation does not necessarily imply signaling during the photon on-flight time.
A description is given of an electron model which makes it possible to simulate pair correlation of random dichotomous signals of the Einstein–Podolsky–Rosen (EPR) type in the Bohm variant. This model can be used to demonstrate that Bell's inequality is satisfied in classical physics. Some features of parametric rf oscillators are used in the model. An analysis of the operation of the model helps one to understand the difference between quantum and classical correlations in EPR experiments. A specific mechanism is suggested for 'nonlocal' control of EPR-type correlations between distant observers, which applies to classical and quantum models. A controlled correlation between two random telegraphic signals is ensured by transmission, to two observers, of a sequence of pulses with the same random phase. An elementary derivation of Bell's inequality is given and an analysis is made of the logic of the use of the popular term 'quantum nonlocality' employed usually in the description of the quantum variants of the investigated experiment.
The quantum theory (QT) and new stochastic approaches have no deterministic prediction for a single measurement or for a single time‐series of events observed for a trapped ion, electron or any other individual physical system. The predictions of QT being of probabilistic character apply to the statistical distribution of the results obtained in various experiments. The Copenhagen interpretation (CI) of QT acknowledged the abstract and statistical character of the predictions of QT but at the same time claimed that a state vector Ψ provided complete description of each individual physical system. The assigning the state vector to an individual physical system together with a postulate of its instantaneous reduction in the measurements was shown by Einstein Podolski and Rosen to lead to so called EPR paradox for the experiments with the entangled pairs of the particles. EPR concluded that a state vector could not provide a complete description of the individual systems and the question arose whether the probabilistic predictions of QT could be derived from some more fundamental spatio‐temporal deterministic description of the invisible sub‐phenomena by introduction of supplementary parameters. The experimental violation of the Bell inequalities in the spin polarization correlation experiments (SPCE) which were the implementations of Bohm and EPR gedanken experiments eliminated so called local and realistic models of the sub‐phenomena. Quite often the violation of these inequalities has been incorrectly interpreted as a proof of the completeness of QT or as the violation of the locality and causality in the micro‐world. The local and realistic models overlooked the fact that an experimental outcome is only the information about a particular system‐system or system‐instrument interaction. Namely the quantum phenomena are described in terms of the probabilities. It is well known that the probability distribution is not an attribute of a dice but it is a characteristic of a whole random experiment: “rolling a dice”. In this paper we will underline: that the quantum probabilities do not describe the lack of knowledge about the physical systems but the lack of knowledge about the experiments and therefore they are “contextual” and that the statistical long range correlations between two random variables X and Y are not a proof of any causal relation between these variables. Moreover any probabilistic model used to described a random experiment is consistent only with a specific protocol telling how the random experiment has to be performed. The probabilistic model used to prove Bell inequalities implied a protocol completely inappropriate and impossible to implement for SPCE . We conclude that the meaningful question about the predictable completeness of QT is still open and it should be answered by a careful and unconventional analysis of the experimental data. The correct understanding of statistical and contextual character of QT is essential for the research in the domain of quantum information and quantum computing.
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a necessary, but not sufficient "symptom" of "true randomness". We base our experimental approach on algorithmic information theory which provides characterizations of algorithmic random sequences in terms of the degrees of incompressibility of their finite prefixes. Algorithmic random sequences are incomputable, but the converse implication is false. We have performed tests of randomness on pseudo-random strings (finite sequences) of length 2322^{32}232 generated with software (Mathematica, Maple), which are cyclic (so, strongly computable), the bits of πππ, which is computable, but not cyclic, and strings produced by quantum measurements (with the commercial device Quantis and by the Vienna IQOQI group). Our empirical tests indicate quantitative differences, some statistically significant, between computable and incomputable sources of "randomness".
We describe an experiment in which two non communicating computers, starting from a common input in the form of sequences of pseudo--random numbers in the interval [0,2π][0,2π][0,2π], and computing deterministic {±1}\{\pm 1\}{±1}--valued functions, chosen at random and independently, produce sequences of numbers whose correlations coincide with the EPR correlations and therefore violate Bell's inequality. The experiment is the practical implementation of a mathematical model of a classical, deterministic system whose initial state is chosen at random from its state space, with a known initial probability distribution, and whose dynamics exhibits the chameleon effect described below. Such a system satisfies the constraints of pre--determination, locality, causality, local independent choices, singlet law and reproduces the EPR correlations.
We start with a review on classical probability representations of quantum states and observables. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The main part of the paper is devoted to the conditional probability model with conditioning on the selection of the pairs of experimental settings. From the viewpoint of quantum foundations, this is a local contextual hidden-variables model. Following the recent works of Dzhafarov and collaborators, we apply our conditional probability approach to characterize (no-)signaling. Consideration of the Bohm–Bell experimental scheme in the presence of signaling is important for applications outside quantum mechanics, e.g., in psychology and social science. The main message of this paper (rooted to Ballentine) is that quantum probabilities and more generally probabilities related to the Bohm–Bell type experiments (not only in physics, but also in psychology, sociology, game theory, economics, and finances) can be classically represented as conditional probabilities.