Local Hidden Variables Research Articles

Realization of Hardy’s Thought Experiment with Photons

We present an experimental realization of Hardy's thought experiment [Phys. Rev. Lett. 68, 2981 (1992)], using photons. The experiment consists of a pair of Mach-Zehnder interferometers that interact through photon bunching at a beam splitter. A striking contradiction is created between the predictions of quantum mechanics and local hidden variables. The contradiction relies on nonmaximally entangled position states of two particles. A Clauser-Horne-type inequality is derived and violated.

POLARIZATION CORRELATIONS IN PAIR PRODUCTION FROM CHARGED AND NEUTRAL STRINGS

Polarization correlations of e+e- pair productions from charged and neutral Nambu strings are investigated, via photon and graviton emissions, respectively and explicit expressions for their corresponding probabilities are derived and found to be speed dependent. The strings are taken to be circularly oscillating closed strings, as perhaps the simplest solution of the Nambu action. In the extreme relativistic case, these probabilities coincide, but, in general, are different, and such inquiries, in principle, indicate whether the string is charged or uncharged. It is remarkable that these dynamical relativistic quantum field theory calculations lead to a clear violation of Local Hidden Variables theories.

Comment on “Separability of quantum states and the violation of Bell-type inequalities”

The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that separable states can violate classical probabilistic constraints is based on a misleading definition of classicality, which is much narrower than Bell's concept of local hidden variables. In a Bell type setting the notion of classicality used by Loubenets corresponds to the assumption of perfect correlations if the same observable is measured on both sides. While it is obvious that most separable states do not satisfy this assumption, this does not constitute "non-classical" behaviour in any usual sense of the word.

Bell’s inequality violation with non-negative Wigner functions

A Bell inequality violation (BIQV) allowed by the two-mode squeezed state (TMSS), whose Wigner function is nonnegative, is shown to hold only for correlations among dynamical variables (DV) that cannot be interpreted via a local hidden variable (LHV) theory. Explicit calculations and interpretation are given for Bell's suggestion that the EPR (Einstein, Podolsky and Rosen) state will not allow for BIQV in conjuction with its Wigner representative state being nonnegative. It is argued that Bell's theorem disallowing the violation of Bell's inequality within a local hidden-variable theory depends on the DV's having a definite value --assigned by the LHV-- even when they cannot be simultaneously measured. The analysis leads us to conclude that BIQV is to be associated with endowing these definite values to the DV's and {\it not} with their locality attributes.

Algorithmic description of hippocampal granule cell dendritic morphology

Recent efforts in computational neuroanatomy have aimed at accurately reproducing all relevant statistical details of dendritic morphology with stochastic models based on local rules and parameters measured from real neurons. Here we present a solution of this problem for dentate gyrus granule cells based on a hidden Markov algorithm. The correctness of the model is supported by the statistical agreement between distributions of emergent parameters measured from population of traced and virtual neurons. The algorithm relies on two local hidden variables, one of which might be associated with dendritic microtubules, and another may represent the time of development.

Quantum World Is Only Smoke and Mirrors

Although I was present at a talk David Mermin gave at MIT in the 1980s, I do not recall the exchange with Victor Weisskopf over the quote from Aage Petersen. I do recall that Weisskopf was sitting in the front row of the audience. After the talk, he said something to the effect that Bell’s theorem is not so surprising, since it only says that quantum mechanics is inconsistent with a local hidden variable theory and that quantum mechanics is intrinsically nonlocal. Much of what people consider the weirdness or paradoxical nature of quantum mechanics, he said, was really due to its nonlocality; people thought that it ought to be local.What I remember most, however, is not Weisskopf’s comment, but a story told by Stephan Berko, my freshman physics professor in 1966–67, who was also in the audience at that talk. After listening to the rather inconclusive discussion among Mermin, Weisskopf, and others, Berko recalled something that Bohr said to him—in fact, the only thing Bohr ever said to him directly. Berko had been visiting the Institute for Theoretical Physics in Copenhagen in 1958 and attended a holiday party, which featured a magic show. After watching some particularly baffling magic tricks, Bohr turned to him and said, “It’s all done with smoke and mirrors!”© 2004 American Institute of Physics.

Speed dependent polarization correlations in QED and entanglement

Exact computations of polarizations correlations probabilities are carried out in QED, to the leading order, for initially polarized as well as unpolarized particles. Quite generally they are found to be speed dependent and are in clear violation of Bells inequality of Local Hidden Variables (LHV) theories. This dynamical analysis shows how speed dependent entangled states are generated. These computations, based on QED are expected to lead to new experiments on polarization correlations monitoring speed in the light of Bells theorem. The paper provides a full QED treatment of the dynamics of entanglement.

Hardy nonlocality via few-body fragmentation imaging

We consider a detection of pair of recoiling reaction fragments, each by its own interferometer, to demonstrate Hardy's contradiction between quantum mechanics and local hidden variables. Our interferometry is based on momentum entanglement and is independent of the identity and internal state of the fragments.

Simulating POVMs on EPR pairs with 5.7 bits of expected communication

We present a classical protocol for simulating correlations obtained by bipartite POVMs on an EPR pair. The protocol uses shared random variables (also known as local hidden variables) augmented by six bits of expected communication.

Proposed optical test of Bell's inequalities not resting upon the fair sampling assumption

Arguments are given against the fair sampling assumption, used to claim an empirical disproof of local realism. New tests are proposed, able to discriminate between quantum mechanics and a restricted, but appealing, family of local hidden-variables models. Such tests require detectors with efficiencies just above 20%.

Proposed optical test of Bell's inequalities not resting upon the fair sampling assumption

Arguments are given against the fair sampling assumption, used to claim an empirical disproof of local realism. New tests are proposed, able to discriminate between quantum mechanics and a restricted, but appealing, family of local hidden-variables models. Such tests require detectors with efficiencies just above 20%.

Violations of Bell inequalities as lower bounds on the communication cost of nonlocal correlations

To reproduce in a local hidden variables theory correlations that violate Bell inequalities, communication must occur between the parties. We show that the amount of violation of a Bell inequality imposes a lower bound on the average communication needed to produce these correlations. Moreover, for every probability distribution there exists an optimal inequality for which the degree of violation gives the minimal average communication. As an example, to produce using classical resources the correlations that maximally violate the Clauser-Horne-Shimony-Holt inequality, $\sqrt{2}\ensuremath{-}1\ensuremath{\simeq}0.4142$ bits of communication are necessary and sufficient. For Bell tests performed on two entangled states of dimension $dg~3$ where each party has the choice between two measurements, our results suggest that more communication is needed to simulate outcomes obtained from certain nonmaximally entangled states than maximally entangled ones.

Communication cost of simulating Bell correlations.

What classical resources are required to simulate quantum correlations? For the simplest and most important case of local projective measurements on an entangled Bell pair state, we show that exact simulation is possible using local hidden variables augmented by just one bit of classical communication. Certain quantum teleportation experiments, which teleport a single qubit, therefore admit a local hidden variables model.

Combinatorics and quantum nonlocality.

We use techniques for lower bounds on communication to derive necessary conditions (in terms of detector efficiency or amount of superluminal communication) for being able to reproduce the quantum correlations occurring in Einstein-Podolsky-Rosen-type experiments with classical local hidden-variable theories. As an application, we consider n parties sharing a Greenberger-Horne-Zeilinger-type state and show that the amount of superluminal classical communication required to reproduce the correlations is at least n(log((2)n-3) bits and the maximum detector efficiency eta(*) for which the resulting correlations can still be reproduced by a local hidden-variable theory is upper bounded by eta(*)</=8/n and thus decreases with n.

THE HESS-PHILIPP MODEL IS NON-LOCAL

Hess and Philipp have constructed what, they claim, is a local hidden variables model reproducing the empirical predictions of quantum mechanics. In this paper explicit expressions for the conditional probabilities for the outcomes of the measurements at the two detectors are calculated. These expressions provide a conclusive demonstration of the falsity of the authors' claim. The authors give two different accounts of their model. The published version omits a crucial detail. As a result it disagrees with quantum mechanics. It also violates signal locality. The unpublished version agrees with quantum mechanics. However, it violates the condition of parameter independence, as Myrvold has previously shown.

No time loophole in Bell's theorem: the Hess-Philipp model is nonlocal.

Hess and Philipp recently claimed [(2001) Proc. Natl. Acad. Sci. USA 98, 14224-14227 and 14228-14233] that proofs of Bell's theorem have overlooked the possibility of time dependence in local hidden variables, hence the theorem has not been proven true. Moreover they present what is claimed to be a local realistic model of the EPR correlations. If this is true then Bell's theorem is not just unproven, but false. We refute both claims. First, we explain why time is not an issue in Bell's theorem, and second, we show that their hidden variables model violates Einstein separability. Hess and Philipp have overlooked the freedom of the experimenter to choose settings of a measurement apparatus at will: any setting could be in force during the same time period.

Quantum nonlocality, Bell inequalities, and the memory loophole

In the analysis of experiments designed to reveal violation of Bell-type inequalities, it is usually assumed that any hidden variables associated with the $n\mathrm{th}$ particle pair would be independent of measurement choices and outcomes for the first $(n\ensuremath{-}1)$ pairs. Models which violate this assumption exploit what we call the memory loophole. We focus on the strongest type of violation, which uses the two-sided memory loophole, in which the hidden variables for pair n can depend on the previous measurement choices and outcomes in both wings of the experiment. We show that the two-sided memory loophole allows a systematic violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality when the data are analyzed in the standard way, but cannot produce a violation if a CHSH expression depending linearly on the data is used. In the first case, the maximal CHSH violation becomes small as the number of particle pairs tested becomes large. Hence, although in principle the memory loophole implies a slight flaw in the existing analyses of Bell experiments, the data still strongly confirm quantum mechanics against local hidden variables. We consider also a related loophole, the simultaneous measurement loophole, which applies if all measurements on each side are carried out simultaneously. We show that this can increase the probability of violating the linearized CHSH inequality as well as other Bell-type inequalities.

Bell s theorem and chemical potential

Chemical potential is a property which involves the effect of interaction between the components of a system, and it results from the whole system. In this paper, we argue that for two particles which have interacted via their spins and are now spatially separated, the so-called Bell's locality condition implies that the chemical potential of each particle is an individual property. Here is a point where quantum statistical mechanics and the local hidden variable theories are in conflict. Based on two distinct concepts of chemical potential, the two theories predict two different patterns for the energy levels of a system of two entangled particles. In this manner, we show how one can distinguish the non-separable features of a two-particle system.

A local hidden variable theory for the GHZ experiment

A recent analysis by de Barros and Suppes of experimentally realizable GHZ correlations supports the conclusion that these correlations cannot be explained by introducing local hidden variables. We show, nevertheless, that their analysis does not exclude local hidden variable models in which the inefficiency in the experiment is an effect not only of random errors in the detector equipment, but is also the manifestation of a pre-set, hidden property of the particles (“prism models”). Indeed, we present an explicit prism model for the GHZ scenario; that is, a local hidden variable model entirely compatible with recent GHZ experiments.

Superluminal influences, hidden variables, and signaling

We consider alternative models to quantum mechanics, that have been proposed in the recent years in order to explain the EPR correlations between two particles. These models allow in principle local hidden variables produced at the source, and some superluminal “hidden communication” (or “influences”) to reproduce the non-local correlations. Moving to the case of three particles, we show that these alternative models lead to signaling when “hidden communication” alone is considered as the origin of the correlations.