343 research outputs found
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 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 modes of a light
field. Then the Bell-CHSH (Clauser, Horne, Shimony and Holt) inequality is
presented for the modes, each of which has a continuous degree of freedom.
Following Mermin's argument, it is demonstrated that for -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 , similarly to the usual -spin cases.Comment: RevTEX; comments are welcomed; new version with minor change
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