Reductions of Hidden Information Sources

In all but special circumstances, measurements of time-dependent processes reflect internal structures and correlations only indirectly. Building predictive models of such hidden information sources requires discovering, in some way, the internal states and mechanisms. Unfortunately, there are often many possible models that are observationally equivalent. Here we show that the situation is not as arbitrary as one would think. We show that generators of hidden stochastic processes can be reduced to a minimal form and compare this reduced representation to that provided by computational mechanics – the ε-machine. On the way to developing deeper, measure-theoretic foundations for the latter, we introduce a new two-step reduction process. The first step (internal-event reduction) produces the smallest observationally equivalent σ-algebra and the second (internal-state reduction) removes σ-algebra components that are redundant for optimal prediction. For several classes of stochastic dynamical systems these reductions produce representations that are equivalent to ε-machines.     

Strengthened Bell inequalities for orthogonal spin directions

We provide bounds on correlations of locally orthogonal observables in two-qubit separable states. These bounds strengthen the Bell inequality and improve upon some alternative entanglement criteria. They provide necessary and sufficient criteria for separability of pure states and test the correlations allowed by local hidden variable models against those allowed by separable quantum states.     

Hidden variable models for quantum theory cannot have any local part

It was shown by Bell that no local hidden variable model is compatible with quantum mechanics. If, instead, one permits the hidden variables to be entirely nonlocal, then any quantum mechanical predictions can be recovered. In this Letter, we consider general hidden variable models which can have both local and nonlocal parts. We show the existence of (experimentally verifiable) quantum correlations that are incompatible with any hidden variable model having a nontrivial local part, such as the model proposed by Leggett.     

Nonlocality is transitive

We show a transitivity property of nonlocal correlations: There exist tripartite nonsignaling correlations of which the bipartite marginals between A and B as well as B and C are nonlocal and any tripartite nonsignaling system between A, B, and C consistent with them must be such that the bipartite marginal between A and C is also nonlocal. This property represents a step towards ruling out certain alternative models for the explanation of quantum correlations such as hidden communication at finite speed. Whereas it is not possible to rule out this model experimentally, it is the goal of our approach to demonstrate this explanation to be logically inconsistent: either the communication cannot remain hidden, or its speed has to be infinite. The existence of a three-party system that is pairwise nonlocal is of independent interest in the light of the monogamy property of nonlocality.     

Necessary and sufficient detection efficiency for the mermin inequalities

We prove that the threshold detection efficiency for a loophole-free Bell experiment using an n-qubit Greenberger-Horne-Zeilinger state and the correlations appearing in the n-partite Mermin inequality is n/(2n-2). If the detection efficiency is equal to or lower than this value, there are local hidden variable models that can simulate all the quantum predictions. If the detection efficiency is above this value, there is no local hidden variable model that can simulate all the quantum predictions.     

Beyond Bell’s Theorem II: Scenarios with Arbitrary Causal Structure

It has recently been found that Bell scenarios are only a small subclass of interesting setups for studying the non-classical features of quantum theory within spacetime. We find that it is possible to talk about classical correlations, quantum correlations and other kinds of correlations on any directed acyclic graph, and this captures various extensions of Bell scenarios that have been considered in the literature. From a conceptual point of view, the main feature of our approach is its high level of unification: while the notions of source, choice of setting and measurement all play seemingly different roles in a Bell scenario, our formalism shows that they are all instances of the same concept of “event”. Our work can also be understood as a contribution to the subject of causal inference with latent variables. Among other things, we introduce hidden Bayesian networks as a generalization of hidden Markov models.     

Finite Local Models for the GHZ Experiment

Some years ago Szabó and Fine proposed a local hidden variable theory for the GHZ experiment based on the assumption that “the detection efficiency is not (only) the effect of random errors in the detector equipment, but it is a more fundamental phenomenon, the manifestation of a predetermined hidden property of the particles”. Szabó and Fine, however, did not provide a general approach to quantum phenomena which avoids nonlocality. Such an approach, based on the same assumption, was instead recently supplied by some of us and called extended semantic realism (ESR) model. We show here that one can extract from the ESR model several local finite models referring to the specific physical situation considered in the GHZ experiment, and that these models can be converted into the toy models for the GHZ experiment worked out by Szabó and Fine.     

Low energy supersymmetry from the heterotic string landscape

We study possible correlations between properties of the observable and hidden sectors in heterotic string theory. Specifically, we analyze the case of the Z6-II orbifold compactification which produces a significant number of models with the spectrum of the supersymmetric standard model. We find that requiring realistic features does affect the hidden sector such that hidden sector gauge group factors SU(4) and SO(8) are favored. In the context of gaugino condensation, this implies low energy supersymmetry breaking.     

Conditional Information and Hidden Correlations in Single-qudit States

We discuss the notions of mutual information and conditional information for noncomposite systems, classical and quantum; both the mutual information and the conditional information are associated with the presence of hidden correlations in the state of a single qudit. We consider analogs of the entanglement phenomena in the systems without subsystems related to strong hidden quantum correlations.     

Two-particle azimuthal and rapidity correlations in intervals of transverse momentum in π+ p-interactions at 250 GeV/c

A multi-dimensional analysis of two-particle correlations in π⁺ p-interactions at 250 GeV/c shows interesting structure. Particularly strong positive shortrange rapidity and azimuthal correlations are observed for low-p _T like sign pairs. This observation is not reproduced by models used for comparison (FRITIOF, DPM, quark gluon (multi)string model). A possible explanation is Bose-Einstein interference not included in these models.     

Structure and Randomness of Continuous-Time,Discrete-Event Processes

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process’ intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects (\(\epsilon \)-machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes.     

Inclusive two-and three-particle rapidity correlations in high-energy hadron-nucleus collisions

Three-particle pseudorapidity correlations are investigated for relativistic secondaries from proton-nucleus interactions at 50, 67, 200 and 400 GeV/c and from pion-nucleus interactions at 50 and 200 GeV/c. The experimental data on two- and three-particle correlations are compared with quantitative predictions of current multiple scattering models of nuclear production. Within these models the influence of various factors on the magnitude of correlations is discussed and it is shown, in particular, that energy-momentum conservation plays an essential role at present accelerator energies.     

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 |ψ|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.     

Invisible axion in the hidden sector of no-scale supergravity

We propose a new axion model which incorporates the U(1)_PQ symmetry into a hidden sector, as well as an observable sector, of no-scale supergravity models. The axion is a spin-zero field in the hidden sector. The U(1)_PQ symmetry is naturally embedded in the family symmetry of the no-scale models. Invisible axions live in the gravity hidden sector without conflict with the cosmological and astrophysical constraints.     

Separability of Quantum States vs. Original Bell (1964) Inequalities

All separable states satisfy all Bell-type inequalities, which involve as their assumption only existence of local realistic (local hidden variable) models of the correlations of spatially separated systems, observed by two or more observers making independent decisions on what to measure (free will). The recent observation by Loubenets, that some separable states do not satisfy the original Bell inequality (1964) has no consequences whatsoever for the studies of the relation of separability with local realism. The original Bell inequality was derived using an additional assumption that the local results for a certain pair of local settings reveal perfect Einstein–Podolsky–Rosen (EPR) correlations. Therefore violation of this inequality by some quantum predictions implies that either (i) the predictions do not allow a local realistic model, or (ii) the predictions do not have the required EPR correlations, or finally both (i) and (ii).     

Analytic solution of a static scale-free network model

We present a detailed analytical study of a paradigmatic scale-free network model, the Static Model. Analytical expressions for its main properties are derived by using the hidden variables formalism. We map the model into a canonic hidden variables one, and solve the latter. The good agreement between our predictions and extensive simulations of the original model suggests that the mapping is exact in the infinite network size limit. One of the most remarkable findings of this study is the presence of relevant disassortative correlations, which are induced by the physical condition of absence of self and multiple connections.     

Objectivity,nonlocality, and the Bell inequalities

It is argued that the Bell inequalities are not a specific feature of local hidden variables theories, but obtain both for local and nonlocal theories that are objectivistic. A nonobjectivistic theory is constructed reproducing the quantum mechanical correlations obtained in realisations of the Einstein-Podolsky-Rosen-Bohm experiment.     

Intriguing electron correlation effects in the photoionization of metallic quantum-dot nanorings

We report detailed results on ionization in metallic quantum-dot (QD) nanorings described by the extended Hubbard model at half filling obtained by exact numerical diagonalization. In spite of very strong electron correlations, the ionization spectra are astonishingly scarce. We attribute this scarcity to a hidden quasi-symmetry, generalizing thereby similar results on optical absorption recently reported [Phys. Rev. B 75, 125323 (2007); 77, 165339 (2008)]. Numerical results indicate that this hidden quasi-symmetry of the extended Hubbard model does not evolve into a true (hidden) symmetry but remains a quasi-symmetry in the case of the restricted Hubbard model as well. Based on the observation on the number of significant ionization signals per each spatial symmetry, we claim the existence of a one-to-one map between the relevant ionization signals of the correlated half-filled nanorings and the one-hole and two-hole-one-particle processes possible in the noninteracting case. Similar to the case of optical absorption, numerous avoided crossings (anticrossings) are present in the ionization spectra, which often involve more than two states. The present results demonstrate that ionization could be a useful tool to study electron correlations in metallic QD-nanoarrays, providing information that is complementary to optical absorption.     

Long range correlations ine + e − annihilation?

We calculate long range multiplicity correlations ine ⁺ e ^? annihilation. Perturbative, probabilistic models predict vanishing multiplicity correlations between two opposite jets, in contrast to the results for non-perturbative models. The former still lead to strong long range correlations within one jet.