Bohm's interpretation and maximally entangled states

Several no-go theorems showed the incompatibility between the locality assumption and quantum correlations obtained from maximally entangled spin states. We analyze these no-go theorems in the framework of Bohm's interpretation. The mechanism by which non-local correlations appear during the results of measurements performed on distant parts of entangled systems is explicitly put into evidence in terms of Bohmian trajectories. It is shown that a GHZ like contradiction of the type+1=-1 occurs for well-chosen initial positions of the Bohmian trajectories and that it is this essential non-classical feature that makes it possible to violate the locality condition.Comment: 18 page

EPR-Bell Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory

We discuss the problem of finding a Lorentz invariant extension of Bohmian mechanics. Due to the nonlocality of the theory there is (for systems of more than one particle) no obvious way to achieve such an extension. We present a model invariant under a certain limit of Lorentz transformations, a limit retaining the characteristic feature of relativity, the non-existence of absolute time resp. simultaneity. The analysis of this model exemplifies an important property of any Bohmian quantum theory: the quantum equilibrium distribution $\rho = |\psi |^2$ cannot simultaneously be realized in all Lorentz frames of reference.Comment: 24 pages, LaTex, 4 figure

Rotationally invariant proof of Bell's theorem without inequalities

The singlet state of two spin-3/2 particles allows a proof of Bell's theorem without inequalities with two distinguishing features: any local observable can be regarded as an Einstein-Podolsky-Rosen element of reality, and the contradiction with local realism occurs not only for some specific local observables but for any rotation whereof.Comment: REVTeX4, 3 page

Bell inequalities as constraints on unmeasurable correlations

The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations , , , and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlation associated to different choices for B. The same analysis applies to the Hardy model and to the "perfect correlations" discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality.Comment: Some modifications have been done in order to improve clarity of presentation and comparison with other approache

Statistics of Atmospheric Correlations

For a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions. Recent advances show that the scope of random matrix theory is much wider. In this work, we show that the random matrix approach can be beneficially applied to a completely different classical domain, namely, to the empirical correlation matrices obtained from the analysis of the basic atmospheric parameters that characterise the state of atmosphere. We show that the spectrum of atmospheric correlation matrices satisfy the random matrix prescription. In particular, the eigenmodes of the atmospheric empirical correlation matrices that have physical significance are marked by deviations from the eigenvector distribution.Comment: 8 pages, 9 figs, revtex; To appear in Phys. Rev.

Hidden variables with nonlocal time

To relax the apparent tension between nonlocal hidden variables and relativity, we propose that the observable proper time is not the same quantity as the usual proper-time parameter appearing in local relativistic equations. Instead, the two proper times are related by a nonlocal rescaling parameter proportional to |psi|^2, so that they coincide in the classical limit. In this way particle trajectories may obey local relativistic equations of motion in a manner consistent with the appearance of nonlocal quantum correlations. To illustrate the main idea, we first present two simple toy models of local particle trajectories with nonlocal time, which reproduce some nonlocal quantum phenomena. After that, we present a realistic theory with a capacity to reproduce all predictions of quantum theory.Comment: 16 pages, accepted for publication in Found. Phys., misprints corrected, references update

Relational Hidden Variables and Non-Locality

We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.Comment: 42 pages in journal style. To appear in Studia Logic

Single-particle nonlocality and entanglement with the vacuum

We propose a single-particle experiment that is equivalent to the conventional two-particle experiment used to demonstrate a violation of Bell's inequalities. Hence, we argue that quantum mechanical nonlocality can be demonstrated by single-particle states. The validity of such a claim has been discussed in the literature, but without reaching a clear consensus. We show that the disagreement can be traced to what part of the total state of the experiment one assigns to the (macroscopic) measurement apparatus. However, with a conventional and legitimate interpretation of the measurement process one is led to the conclusion that even a single particle can show nonlocal properties.Comment: 6 pages, 5 figure

Information Invariance and Quantum Probabilities

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as in quantum theory follows essentially from the assumption that all physical states of a higher dimensional system are those and only those from which one can post-select physical states of two-dimensional systems. The requirement that no more than one bit of information (as quantified by the quadratic measure) is contained in all possible post-selected two-dimensional systems is equivalent to the positivity of density operator in quantum theory.Comment: 8 pages, 1 figure. This article is dedicated to Pekka Lahti on the occasion of his 60th birthday. Found. Phys. (2009

Greenberger-Horne-Zeilinger nonlocality for continuous variable systems

As a development of our previous work, this paper is concerned with the Greenberger-Horne-Zeilinger (GHZ) nonlocality for continuous variable cases. The discussion is based on the introduction of a pseudospin operator, which has the same algebra as the Pauli operator, for each of the $N$ modes of a light field. Then the Bell-CHSH (Clauser, Horne, Shimony and Holt) inequality is presented for the $N$ modes, each of which has a continuous degree of freedom. Following Mermin's argument, it is demonstrated that for $N$-mode parity-entangled GHZ states (in an infinite-dimensional Hilbert space) of the light field, the contradictions between quantum mechanics and local realism grow exponentially with $N$, similarly to the usual $N$-spin cases.Comment: RevTEX; comments are welcomed; new version with minor change