scholarly journals Is Einsteinian no-signalling violated in Bell tests?

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 739-753 ◽  
Author(s):  
Marian Kupczynski
Keyword(s):  
Quantum Electrodynamics ◽  
Probability Distributions ◽  
Selection Procedure ◽  
Quantum Correlations ◽  
Spin Projection ◽  
Marginal Probability ◽  
Strong Correlations ◽  
Relativistic Invariance ◽  
Long Range Correlations ◽  
Apparent Violation

AbstractRelativistic invariance is a physical law verified in several domains of physics. The impossibility of faster than light influences is not questioned by quantum theory. In quantum electrodynamics, in quantum field theory and in the standard model relativistic invariance is incorporated by construction. Quantum mechanics predicts strong long range correlations between outcomes of spin projection measurements performed in distant laboratories. In spite of these strong correlations marginal probability distributions should not depend on what was measured in the other laboratory what is called shortly: non-signalling. In several experiments, performed to test various Bell-type inequalities, some unexplained dependence of empirical marginal probability distributions on distant settings was observed. In this paper we demonstrate how a particular identification and selection procedure of paired distant outcomes is the most probable cause for this apparent violation of no-signalling principle. Thus this unexpected setting dependence does not prove the existence of superluminal influences and Einsteinian no-signalling principle has to be tested differently in dedicated experiments. We propose a detailed protocol telling how such experiments should be designed in order to be conclusive. We also explain how magical quantum correlations may be explained in a locally causal way.

scholarly journals Monogamy of non-local quantum correlations

2008 ◽  
Vol 465 (2101) ◽  
pp. 59-69 ◽  
Author(s):  
Ben Toner
Keyword(s):  
Probability Distributions ◽  
Bell Inequality ◽  
Arbitrary Dimension ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Interactive Proof ◽  
Proof Systems ◽  
Non Local ◽  
A New Technique ◽  
Tsirelson Bound

We describe a new technique for obtaining Tsirelson bounds, which are upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signalling, we obtain a Tsirelson bound by maximizing over all no-signalling probability distributions. This maximization can be cast as a linear programme. In a setting where three parties, A, B and C, share an entangled quantum state of arbitrary dimension, we (i) bound the trade-off between AB's and AC's violation of the Clauser–Horne–Shimony–Holt inequality and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities, relevant for interactive proof systems and cryptography.

The Discrete Optimal Assignment Problem

2016 ◽  
Author(s):  
Alfred Galichon
Keyword(s):  
Linear Programming ◽  
Assignment Problem ◽  
Linear Programming Problem ◽  
Matrix Algebra ◽  
Probability Distributions ◽  
Marginal Probability ◽  
Finite Support ◽  
Complementary Slackness ◽  
Finite Dimensional ◽  
Finite Dimensional Case

This chapter considers the finite-dimensional case, which is the case when the marginal probability distributions are discrete with finite support. In this case, the Monge–Kantorovich problem becomes a finite-dimensional linear programming problem; the primal and the dual solutions are related by complementary slackness, which is interpreted in terms of stability. The solutions can be conveniently computed by linear programming solvers, and the chapter shows how this is done using some matrix algebra and Gurobi.

On the gauge and relativistic invariance in quantum electrodynamics

1965 ◽  
Vol 40 (1) ◽  
pp. 319-322
Author(s):  
J. N. Chahoud ◽  
G. Russo
Keyword(s):  
Quantum Electrodynamics ◽  
Relativistic Invariance

scholarly journals Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 185 ◽  
Author(s):  
Yeong-Cherng Liang ◽  
Yanbao Zhang
Keyword(s):  
Hypothesis Testing ◽  
Hypothesis Test ◽  
Quantum Correlations ◽  
Ratio Method ◽  
Empirical Observation ◽  
Hidden Variable ◽  
Apparent Violation ◽  
Hidden Variable Theories ◽  
Experimental Trials ◽  
Local Hidden Variable

The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell’s seminal work to distinguish, via a Bell test, quantum correlations from the set of correlations allowed by local-hidden-variable theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this paper, we show that the prediction-based-ratio method—initially developed for performing a hypothesis test of local-hidden-variable theories—can equally well be applied to test many other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce any of the outer approximation to the quantum set of correlations due to Navascués-Pironio-Acín. We numerically simulate Bell tests using hypothetical nonlocal sources of correlations to illustrate the applicability of the method in both the independent and identically distributed (i.i.d.) scenario and the non-i.i.d. scenario. As a further application, we demonstrate how this method allows us to unveil an apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. This, in turn, highlights the importance of the randomization of measurement settings, as well as a consistency check of the nonsignaling conditions in a Bell test.

scholarly journals Quantum correlations are weaved by the spinors of the Euclidean primitives

2018 ◽  
Vol 5 (5) ◽  
pp. 180526 ◽  
Author(s):  
Joy Christian
Keyword(s):  
Conformal Geometry ◽  
General Theorem ◽  
Three Dimensional ◽  
Physical Space ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Theoretical Physics ◽  
Strong Correlations ◽  
Algebraic Representation ◽  
Closed Set

The exceptional Lie group E 8 plays a prominent role in both mathematics and theoretical physics. It is the largest symmetry group associated with the most general possible normed division algebra, namely, that of the non-associative real octonions, which—thanks to their non-associativity—form the only possible closed set of spinors (or rotors) that can parallelize the 7-sphere. By contrast, here we show how a similar 7-sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes and volumes, which characterize the three-dimensional conformal geometry of the ambient physical space, set within its eight-dimensional Clifford-algebraic representation. Remarkably, the resulting algebra remains associative, and allows us to understand the origins and strengths of all quantum correlations locally, in terms of the geometry of the compactified physical space, namely, that of a quaternionic 3-sphere, S 3 , with S 7 being its algebraic representation space. Every quantum correlation can thus be understood as a correlation among a set of points of this S 7 , computed using manifestly local spinors within S 3 , thereby extending the stringent bounds of ±2 set by Bell inequalities to the bounds of ± 2 2 on the strengths of all possible strong correlations, in the same quantitatively precise manner as that predicted within quantum mechanics. The resulting geometrical framework thus overcomes Bell’s theorem by producing a strictly deterministic and realistic framework that allows a locally causal understanding of all quantum correlations, without requiring either remote contextuality or backward causation. We demonstrate this by first proving a general theorem concerning the geometrical origins of the correlations predicted by arbitrarily entangled quantum states, and then reproducing the correlations predicted by the EPR-Bohm and the GHZ states. The raison d’être of strong correlations turns out to be the Möbius-like twists in the Hopf bundles of S 3 and S 7 .

Revealing a temporal symmetry/asymmetry dichotomy in a Markovian setting, and a parameterization based on fractional low-order joint moments

2020 ◽  
Author(s):  
Alin Andrei Carsteanu ◽  
Andreas Langousis
Keyword(s):  
Stochastic Process ◽  
Probability Distributions ◽  
Arrow Of Time ◽  
Marginal Probability ◽  
Joint Moments ◽  
Statistical Tool ◽  
Joint Distributions ◽  
Striking Result ◽  
Temporal Symmetry ◽  
Low Order

<p>We show that "an arrow of time", which is reflected by the joint distributions of successive variables in a stochastic process, may exist (or not) solely on grounds of marginal probability distributions, without affecting stationarity or involving the structural dependencies within the process. The temporal symmetry/asymmetry dichotomy thus revealed, is exemplified for the simplest case of stably-distributed Markovian recursions, where the lack of Gaussianity, even when the increments of the process are independent and identically distributed (i.i.d.) with symmetric marginal, is generating a break of temporal symmetry. We devise a statistical tool to evidence this striking result, based on fractional low-order joint moments, whose existence is guaranteed even for the case of "fat-tailed" strictly-stable distributions, and is thereby suited for parameterizing structural dependencies within such a process.</p>

Parameterization of multifractal cascade models based on their breakdown coefficients

2020 ◽  
Author(s):  
César Aguilar Flores ◽  
Alin Andrei Carsteanu
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Rainfall Intensity ◽  
Probability Distributions ◽  
Asymptotic Properties ◽  
Distribution Functions ◽  
Marginal Probability ◽  
Probability Distribution Functions ◽  
Marginal Probability Distribution ◽  
Cascade Models

<p>Breakdown coefficients of multifractal cascades have been shown, in various contexts, to be ergodic in their (marginal) probability distribution functions, however the necessary connection between the cascading process (or a tracer thereof, such as rainfall) and the breakdown coefficients of the measure generated by the cascade, was missing. This work presents a method of parameterization of certain types of multiplicative cascades, using the breakdown coefficients of the measures they generate. The method is based on asymptotic properties of the probability distributions of the breakdown coefficients in “dressed” cascades, as compared with the respective distributions of the cascading weights. An application to rainfall intensity time series is presented.</p>

scholarly journals Entropy Analysis in Relativistic Heavy-Ion Collisions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shakeel Ahmad ◽  
A. Ahmad ◽  
Anuj Chandra ◽  
M. Zafar ◽  
M. Irfan
Keyword(s):  
Phase Space ◽  
Heavy Ion ◽  
Relativistic Heavy Ion Collisions ◽  
Strong Correlations ◽  
Entropy Analysis ◽  
Multiphase Transport ◽  
Long Range Correlations ◽  
Ion Collisions ◽  
Full Phase Space ◽  
Multiparticle System

Entropy creation in multiparticle system is investigated by analysing the experimental data on ion-ion collisions at AGS and SPS energies and the results thus obtained are compared with those predicted by multiphase transport and correlation-free Monte Carlo models. Entropies produced in limited- and full-phase space are observed to increase with increasing beam energy. The entropy values, normalized to the maximum rapidity and plotted against pseudorapidity (bin width also normalized to the maximum rapidity), are found to be energy independent, exhibiting a kind of entropy scaling. Such scaling is observed in the full phase space as well as in the regions confined to the forward or backward hemispheres. The findings also reveal that there exist strong correlations amongst the particles produced in the forward and backward hemispheres around the midrapidity. These correlations are found to be of short range in nature, and the contributions from the long-range correlations seem to be absent. PACS numbers: 25.75-q, 25.75.Gz.

scholarly journals Experimental Connection between the Instrumental and Bell Inequalities

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 27
Author(s):  
Iris Agresti ◽  
Gonzalo Carvacho ◽  
Davide Poderini ◽  
Leandro Aolita ◽  
Rafael Chaves ◽  
...  
Keyword(s):  
Causal Model ◽  
Probability Distributions ◽  
Causal Structure ◽  
Joint Probability ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Causal Processes ◽  
Chsh Inequality ◽  
Joint Probability Distributions ◽  
Selection Of

An investigated process can be studied in terms of the causal relations among the involved variables, representing it as a causal model. Some causal models are particularly relevant, since they can be tested through mathematical constraints between the joint probability distributions of the observables. This is a valuable tool because, if some data violates the constraints of a causal model, the implication is that the observed statistics is not compatible with that causal structure. Strikingly, when non-classical correlations come to play, a discrepancy between classical and quantum causal predictions can arise, producing a quantum violation of the classical causal constraints. The simplestscenario admitting such quantum violation is given by the instrumental causal processes. Here, we experimentally violate an instrumental test on a photonic platform and show how the quantum correlations violating the CHSH inequality can be mapped into correlations violating an instrumental test, despite the different forms of non-locality they display. Indeed, starting from a Bell-like scenario, we recover the violation of the instrumental scenario through a map between the two behaviours, which includes a post-selection of data and then we test an alternative way to violate the CHSH inequality, adopting the instrumental process platform.

A Method Based on Taking the Average of Probabilities to Compute the Flow Duration Curve

2000 ◽  
Vol 31 (3) ◽  
pp. 187-206 ◽  
Author(s):  
Hikmet Kerem Cigizoglu
Keyword(s):  
Probability Distributions ◽  
Maximum Flow ◽  
Exceedance Probability ◽  
Flow Duration Curve ◽  
Marginal Probability ◽  
Lognormal Distributions ◽  
Type Iii ◽  
Flow Duration ◽  
Pearson Type ◽  
Flow Duration Curves

In this study a method based on taking the average of the probabilities is presented to obtain flow duration curve. In this method the exceedance probability for each flow value is computed repeatedly for all time periods within a year. The final representing exceedance is just simply the average of all these probabilities. The applicability of the method to daily mean flows is tested assuming various marginal probability distributions like normal, Pearson type III, log-Pearson type III, 2-parameter lognormal and 3-parameter lognormal distributions. It is seen that the observed flow duration curves were quite well approximated by the 2-parameter lognormal average of probabilities curves. In that case the method requires the computation of the daily mean and standard deviation values of the observed flow data. The method curve enables extrapolation of the available data providing the exceedance probabilities for the flows higher than the observed maximum flow. The method is applied to the missing data and ungauged site problems and the results are quite satisfactory.

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