Massimo Regoli

ON THE EPR–CHAMELEON EXPERIMENT

We construct a family of classical deterministic dynamical systems (triples formed by a state space, an initial distribution, a dynamics) parametrized by pairs of vectors (a,b) in the unit circle in ℝ2. The systems describe pairs of particles and the dynamics is strictly local, i.e. the dynamics of particle j=1,2 depends only on one of the two unit vectors, but not the other. To each particle one associates a family of ± 1-valued observables (j = 1,2), also parametrized by vectors a in the unit circle in ℝ2. Moreover we assume that, if observable is measured on particle j=1,2, then the dynamics of this particle will be (chameleon effect). Using these ingredients we prove that the dynamics and the initial distributions of the given systems can be chosen in such a way that, if the observable is measured on particle j=1,2, then the EPR correlations -cos(a1-a2) are reproduced. This theoretical construction is then used to realize the following experiment: a central computer S (source) sends the same signal to two local computers A and B. After receiving the signal A (resp. B), chooses one vector a (resp. b) in the unit circle in ℝ2 and computes the value of the corresponding observable (resp. ). These values are uniquely defined by the deterministic dynamics and the choices are independent of one another. The local computers send back to the central one the results of the evaluation of these ±1-valued functions and the central computer evaluates the empirical correlations according to the usual statistical rules. As a result the EPR correlations are reproduced with very good approximation and the Bell inequality is violated by a classical, macroscopic deterministic system performing purely local choices. The program to run the experiment is available from http://volterra.mat.uniroma2.it

Non-Locality and Quantum Theory: New Experimental Evidence

Starting from the late 60’s many experiments have been performed to verify the violation Bell’s inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell’s inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell’s inequality. The conclusions of the present experiment are: (I) no contradiction between quantum theory and locality can be deduced from the violation of Bell’s inequality. (II) The Copenhagen interpretation of quantum theory becomes quite reasonable and not metaphyisic if interpreted at the light of the chameleon effect. (III) One can realize quantum entanglement by classical computers.

On a class of strongly asymmetric PKA algorithms

Abstract In the papers [New features for public key exchange algorithms, in: 18-th International ICWG Meeting (Krakow 2011)], [Strongly asymmetric PKD cryptographic algorithms: An implementation using the matrix model, in: Proceedings ISEC Conference (Shizuoka 2011)] a new scheme to produce public key agreement (PKA) algorithms was proposed and some examples based on polynomials (toy models) were discussed. In the present paper we introduce a non-commutative realization of the above mentioned scheme and prove that non-commutativity can be an essential ingredient of security in the sense that, in the class of algorithms constructed, under some commutativity assumptions on the matrices involved, we can find a breaking strategy, but dropping these assumptions we can not, even if we assume, as we do in all the attacks discussed in the present paper, that discrete logarithms have zero cost.

Note on the EPR-Chameleon experiment

In the past 20 years quantum probability has challanged the widespread belief that classical macroscopic systems cannot, by local independent choices, produce sequences of data whose correlations violate Bell’s inequality. The possibility of such a violation is not a matter of interpretation, but of fact: “local independent choices” means that two separated and non communicating experimenters make measurements but one does not know what the other measures (or even if the other one measures something); correlations are evaluated by means of standard procedures. The present experiment shows that this is not the case: in no way the EPR correlations and related experiments can be considered as a support of the incompatibility of quantum theory with local realistic theories, in particular relativity.

QUANTUM PROBABILITY AND THE INTERPRETATION OF QUANTUM MECHANICS: A CRUCIAL EXPERIMENT

In the past few years the quantum probabilistic point of view on the foundations of quantum theory has been subject to critiques from several sides. Some of these1 are based on arguments which, although wrong2, still remain within the usual framework of scientific debate; some others, altough more pertinent to the domain of rethoric or of sociology than to science, might nevertheless have some interest as examples of that “scientific irrationalism” which was object of impotent irony in3 (examples are4 and even more the arguments, used by the director of “Le Scienze”(1) Prof. Enrico Bellone, to deny to the supporters of quantum probability the rights of expression he gave to its opponents: those interested in this and other examples of “sociology of academic repression” may consult the Volterra Center’s WEB page: http://volterra.mat.uniroma2.it.)