scholarly journals Experimental test of nonlocal causality

2016 ◽  
Vol 2 (8) ◽  
pp. e1600162 ◽  
Author(s):  
Martin Ringbauer ◽  
Christina Giarmatzi ◽  
Rafael Chaves ◽  
Fabio Costa ◽  
Andrew G. White ◽  
...  
Keyword(s):  
Broad Class ◽  
Type Inequality ◽  
Quantum Correlations ◽  
Empirical Science ◽  
Local Models ◽  
Causal Explanations ◽  
Causal Influence ◽  
Quantum Particles ◽  
Outcome Dependence ◽  
Special Case

Explaining observations in terms of causes and effects is central to empirical science. However, correlations between entangled quantum particles seem to defy such an explanation. This implies that some of the fundamental assumptions of causal explanations have to give way. We consider a relaxation of one of these assumptions, Bell’s local causality, by allowing outcome dependence: a direct causal influence between the outcomes of measurements of remote parties. We use interventional data from a photonic experiment to bound the strength of this causal influence in a two-party Bell scenario, and observational data from a Bell-type inequality test for the considered models. Our results demonstrate the incompatibility of quantum mechanics with a broad class of nonlocal causal models, which includes Bell-local models as a special case. Recovering a classical causal picture of quantum correlations thus requires an even more radical modification of our classical notion of cause and effect.

scholarly journals Cyclic quantum causal models

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jonathan Barrett ◽  
Robin Lorenz ◽  
Ognyan Oreshkov
Keyword(s):  
Causal Reasoning ◽  
Causal Structure ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Causal Models ◽  
Causal Order ◽  
Quantum Processes ◽  
Causal Explanations ◽  
Causal Structures

AbstractCausal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory encompassing quantum systems and gravity is expected to allow causally nonseparable processes featuring operations in indefinite causal order, defying that events be causally ordered at all. The first challenge has been addressed through the recent development of intrinsically quantum causal models, allowing causal explanations of quantum processes – provided they admit a definite causal order, i.e. have an acyclic causal structure. This work addresses causally nonseparable processes and offers a causal perspective on them through extending quantum causal models to cyclic causal structures. Among other applications of the approach, it is shown that all unitarily extendible bipartite processes are causally separable and that for unitary processes, causal nonseparability and cyclicity of their causal structure are equivalent.

A Bi-Directional Reflectance Function for Woven Textiles

1998 ◽  
Author(s):  
Brad Hunting ◽  
Stephen Derby ◽  
Raymond Puffer
Keyword(s):  
Surface Properties ◽  
Broad Class ◽  
Fiber Surface ◽  
Anisotropic Model ◽  
Reflectance Function ◽  
Function Models ◽  
Woven Textile ◽  
Special Case ◽  
Reflectance Data ◽  
Directional Reflectance

Abstract This paper presents a novel bi-directional reflectance function for woven textile substrates. The new reflectance function models a broad class of woven substrates, including substrates with significant anisotropic reflectance. Isotropic behavior is handled as a special case of the anisotropic model. The new model recognizes fiber surface properties, thread geometry, and weave geometry. Experimental reflectance data is presented.

scholarly journals On a New Half-Discrete Hilbert-Type Inequality Involving the Variable Upper Limit Integral and Partial Sums

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 229 ◽  
Author(s):  
Jianquan Liao ◽  
Shanhe Wu ◽  
Bicheng Yang
Keyword(s):  
Type Inequality ◽  
Constant Factor ◽  
Partial Sums ◽  
Upper Limit ◽  
The Best Possible Constant ◽  
Special Case ◽  
Equivalent Conditions ◽  
Hilbert Type

In this paper we establish a new half-discrete Hilbert-type inequality involving the variable upper limit integral and partial sums. As applications, an inequality obtained from the special case of the half-discrete Hilbert-type inequality is further investigated; moreover, the equivalent conditions of the best possible constant factor related to several parameters are proved.

Implications of latent trajectory models for the study of developmental psychopathology

2003 ◽  
Vol 15 (3) ◽  
pp. 581-612 ◽  
Author(s):  
PATRICK J. CURRAN ◽  
MICHAEL T. WILLOUGHBY
Keyword(s):  
Developmental Psychopathology ◽  
Broad Class ◽  
Theoretical Models ◽  
Developmental Theory ◽  
Empirical Science ◽  
Quantitative Methodology ◽  
Growth Curve Models ◽  
Latent Trajectory ◽  
Trajectory Models ◽  
The One

The field of developmental psychopathology is faced with a dual challenge. On the one hand, we must build interdisciplinary theoretical models that adequately reflect the complexity of normal and abnormal human development over time. On the other hand, to remain a viable empirical science, we must rigorously evaluate these theories using statistical methods that fully capture this complexity. The degree to which our statistical models fail to correspond to our theoretical models undermines our ability to validly test developmental theory. The broad class of random coefficient trajectory (or growth curve) models allow us to test our theories in ways not previously possible. Despite these advantages, there remain certain limits with regard to the types of questions these models can currently evaluate. We explore these issues through the pursuit of three goals. First, we provide an overview of a variety of trajectory models that can be used for rigorously testing many hypotheses in developmental psychopathology. Second, we highlight what types of research questions are well tested using these methods and what types of questions currently are not. Third, we describe areas for future statistical development and encourage the ongoing interchange between developmental theory and quantitative methodology.

scholarly journals Towards a unified theory of fractional and nonlocal vector calculus

2021 ◽  
Vol 24 (5) ◽  
pp. 1301-1355
Author(s):  
Marta D’Elia ◽  
Mamikon Gulian ◽  
Hayley Olson ◽  
George Em Karniadakis
Keyword(s):  
Ad Hoc ◽  
Broad Class ◽  
Anomalous Behavior ◽  
Unified Theory ◽  
Constrained Problems ◽  
Vector Calculus ◽  
Weighted Laplacian ◽  
Classical Vector ◽  
Laplacian Operators ◽  
Special Case

Abstract Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green’s identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fractional vector calculus have been put forward. Some have been studied rigorously and in depth, while others have been introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green’s identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. The proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus.

Causation and Statistical Inference

2010 ◽  
Author(s):  
Clark Glymour
Keyword(s):  
Risk Factors ◽  
Dimension Reduction ◽  
Statistical Inference ◽  
Statistical Models ◽  
Causal Interpretation ◽  
Causal Relations ◽  
Causal Explanations ◽  
Causal Influence

In the applied statistical literature, causal relations are often described equivocally or euphemistically as ‘risk factors’, or as part of ‘dimension reduction’. The statistical literature also tends to speak of ‘statistical models’ rather than of causal explanations, and to say that parameters of a model are ‘interpretable’, often means that the parameters make sense as measures of causal influence. These ellipses are due in part to the use of statistical formalisms for which a causal interpretation is wanted but unavailable or unfamiliar, and in part to a philosophical distrust of attributions of causation outside experimental contexts, misgivings traceable to the disciplinary institutionalization of claims of influential statisticians, notably Karl Pearson and Ronald Fisher. More candid treatments of causal relations have recently emerged in the theoretical statistical literature.

scholarly journals Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-Type Inequalities for Markov Chains and Related Processes

2014 ◽  
Vol 51 (4) ◽  
pp. 1100-1113 ◽  
Author(s):  
Aryeh Kontorovich ◽  
Roi Weiss
Keyword(s):  
Markov Chains ◽  
Elementary Proof ◽  
Broad Class ◽  
Type Inequality ◽  
Concentration Inequality ◽  
State Spaces ◽  
Measure Concentration ◽  
Chernoff Bound ◽  
Countably Infinite ◽  
Infinite State

We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of noncontracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a short, elementary proof of a general concentration inequality for Markov and hidden Markov chains, which supersedes some of the known results and easily extends to other processes such as Markov trees. As applications, we provide a Dvoretzky-Kiefer-Wolfowitz-type inequality and a uniform Chernoff bound. All of our bounds are dimension-free and hold for countably infinite state spaces.

scholarly journals Multipartite quantum correlations and local recoverability

2015 ◽  
Vol 471 (2177) ◽  
pp. 20140941 ◽  
Author(s):  
Mark M. Wilde
Keyword(s):  
Quantum Correlations ◽  
Entanglement Measure ◽  
Physical Systems ◽  
Strong Subadditivity ◽  
Link Type ◽  
Total Correlation ◽  
Symmetric Quantum ◽  
Operational Interpretation ◽  
Open Question ◽  
Special Case

Characterizing genuine multipartite quantum correlations in quantum physical systems has historically been a challenging problem in quantum information theory. More recently, however, the total correlation or multipartite information measure has been helpful in accomplishing this goal, especially with the multipartite symmetric quantum (MSQ) discord (Piani et al. 2008 Phys. Rev. Lett. 100, 090502. ( doi:10.1103/PhysRevLett.100.090502 )) and the conditional entanglement of multipartite information (CEMI) (Yang et al. 2008 Phys. Rev. Lett. 101, 140501. ( doi:10.1103/PhysRevLett.101.140501 )). Here, we apply a recent and significant improvement of strong subadditivity of quantum entropy (Fawzi & Renner 2014 ( http://arxiv.org/abs/1410.0664 )) in order to develop these quantities further. In particular, we prove that the MSQ discord is nearly equal to zero if and only if the multipartite state for which it is evaluated is approximately locally recoverable after performing measurements on each of its systems. Furthermore, we prove that the CEMI is a faithful entanglement measure, i.e. it vanishes if and only if the multipartite state for which it is evaluated is a fully separable state. Along the way, we provide an operational interpretation of the MSQ discord in terms of the partial state distribution protocol, which in turn, as a special case, gives an interpretation for the original discord quantity. Finally, we prove an inequality that could potentially improve upon the Fawzi–Renner inequality in the multipartite context, but it remains an open question to determine whether this is so.

scholarly journals Quantum violation of the pigeonhole principle and the nature of quantum correlations

2016 ◽  
Vol 113 (3) ◽  
pp. 532-535 ◽  
Author(s):  
Yakir Aharonov ◽  
Fabrizio Colombo ◽  
Sandu Popescu ◽  
Irene Sabadini ◽  
Daniele C. Struppa ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Effects ◽  
Quantum Correlations ◽  
Fundamental Principle ◽  
Pigeonhole Principle ◽  
Quantum Particles ◽  
Interesting Structure

The pigeonhole principle: “If you put three pigeons in two pigeonholes, at least two of the pigeons end up in the same hole,” is an obvious yet fundamental principle of nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above “quantum pigeonhole principle” is only one of a host of related quantum effects, and points to a very interesting structure of quantum mechanics that was hitherto unnoticed. Our results shed new light on the very notions of separability and correlations in quantum mechanics and on the nature of interactions. It also presents a new role for entanglement, complementary to the usual one. Finally, interferometric experiments that illustrate our effects are proposed.

scholarly journals Condition for zero and nonzero discord in graph Laplacian quantum states

2019 ◽  
Vol 17 (02) ◽  
pp. 1950018 ◽  
Author(s):  
Supriyo Dutta ◽  
Bibhas Adhikari ◽  
Subhashish Banerjee
Keyword(s):  
Quantum Mechanics ◽  
Quantum Discord ◽  
Graph Laplacian ◽  
Quantum Correlations ◽  
Quantum States ◽  
Simple Graphs ◽  
Graph Theoretic ◽  
Weighted Directed Graph ◽  
Special Case ◽  
Qubit States

This work is at the interface of graph theory and quantum mechanics. Quantum correlations epitomize the usefulness of quantum mechanics. Quantum discord is an interesting facet of bipartite quantum correlations. Earlier, it was shown that every combinatorial graph corresponds to quantum states whose characteristics are reflected in the structure of the underlined graph. A number of combinatorial relations between quantum discord and simple graphs were studied. To extend the scope of these studies, we need to generalize the earlier concepts applicable to simple graphs to weighted graphs, corresponding to a diverse class of quantum states. To this effect, we determine the class of quantum states whose density matrix representation can be derived from graph Laplacian matrices associated with a weighted directed graph and call them graph Laplacian quantum states. We find the graph theoretic conditions for zero and nonzero quantum discord for these states. We apply these results on some important pure two qubit states, as well as a number of mixed quantum states, such as the Werner, Isotropic, and [Formula: see text]-states. We also consider graph Laplacian states corresponding to simple graphs as a special case.

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