scholarly journals Analysing causal structures in generalised probabilistic theories

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 236 ◽  
Author(s):  
Mirjam Weilenmann ◽  
Roger Colbeck
Keyword(s):  
Classical Theory ◽  
Convex Cone ◽  
Causal Explanation ◽  
Causal Structure ◽  
Quantum Mechanical ◽  
Probabilistic Theory ◽  
Special Cases ◽  
Classical Quantum ◽  
Causal Structures ◽  
Probabilistic Theories

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad range of theories, which include both quantum and classical theory as special cases. We propose a method for analysing differences between such theories based on the so-called measurement entropy. We apply this method to several causal structures, deriving new relations that separate classical, quantum and more general theories within these causal structures. The constraints we derive for the most general theories are in a sense minimal requirements of any causal explanation in these scenarios. In addition, we make several technical contributions that give insight for the entropic analysis of quantum causal structures. In particular, we prove that for any causal structure and for any generalised probabilistic theory, the set of achievable entropy vectors form a convex cone.

scholarly journals The Inflation Technique Completely Solves the Causal Compatibility Problem

2020 ◽  
Vol 8 (1) ◽  
pp. 70-91 ◽  
Author(s):  
Miguel Navascués ◽  
Elie Wolfe
Keyword(s):  
Linear Programming ◽  
Latent Variables ◽  
Causal Explanation ◽  
Causal Structure ◽  
Categorical Variables ◽  
False Negatives ◽  
The Given ◽  
Causal Structures ◽  
Compatibility Question ◽  
Structure Graph

AbstractThe causal compatibility question asks whether a given causal structure graph — possibly involving latent variables — constitutes a genuinely plausible causal explanation for a given probability distribution over the graph’s observed categorical variables. Algorithms predicated on merely necessary constraints for causal compatibility typically suffer from false negatives, i.e. they admit incompatible distributions as apparently compatible with the given graph. In 10.1515/jci-2017-0020, one of us introduced the inflation technique for formulating useful relaxations of the causal compatibility problem in terms of linear programming. In this work, we develop a formal hierarchy of such causal compatibility relaxations. We prove that inflation is asymptotically tight, i.e., that the hierarchy converges to a zero-error test for causal compatibility. In this sense, the inflation technique fulfills a longstanding desideratum in the field of causal inference. We quantify the rate of convergence by showing that any distribution which passes the nth-order inflation test must be $\begin{array}{} \displaystyle {O}{\left(n^{{{-}{1}}/{2}}\right)} \end{array}$-close in Euclidean norm to some distribution genuinely compatible with the given causal structure. Furthermore, we show that for many causal structures, the (unrelaxed) causal compatibility problem is faithfully formulated already by either the first or second order inflation test.

scholarly journals Experimental entanglement of temporal order

Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 621
Author(s):  
Giulia Rubino ◽  
Lee A. Rozema ◽  
Francesco Massa ◽  
Mateus Araújo ◽  
Magdalena Zych ◽  
...  
Keyword(s):  
Experimental Data ◽  
Experimental Evidence ◽  
Temporal Order ◽  
Causal Structure ◽  
Physical Processes ◽  
Physical Constraints ◽  
Quantum Description ◽  
Causal Processes ◽  
Causal Structures ◽  
Probabilistic Theories

The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. Here, we present the first demonstration of indefinite temporal order outside of quantum formalism. We show that our experimental outcomes are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, we derive physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. We then experimentally invalidate these theories by violating the inequality using entangled temporal order. This provides experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.

scholarly journals Quantum violations in the Instrumental scenario and their relations to the Bell scenario

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 186 ◽  
Author(s):  
Thomas Van Himbeeck ◽  
Jonatan Bohr Brask ◽  
Stefano Pironio ◽  
Ravishankar Ramanathan ◽  
Ana Belén Sainz ◽  
...  
Keyword(s):  
Opposite Direction ◽  
Causal Structure ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Causal Models ◽  
Classical Quantum ◽  
Bell Nonlocality ◽  
Causal Structures

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.

The Causal Structure of Suppressor Variables

2019 ◽  
Vol 44 (4) ◽  
pp. 367-389 ◽  
Author(s):  
Yongnam Kim
Keyword(s):  
Instrumental Variables ◽  
Regression Models ◽  
Predictive Power ◽  
Causal Explanation ◽  
Causal Structure ◽  
Criterion Variable ◽  
Psychological Measurement ◽  
Causal Structures ◽  
Discovery Algorithms ◽  
Suppression Effects

Suppression effects in multiple linear regression are one of the most elusive phenomena in the educational and psychological measurement literature. The question is, How can including a variable, which is completely unrelated to the criterion variable, in regression models significantly increase the predictive power of the regression models? In this article, we view suppression from a causal perspective and uncover the causal structure of suppressor variables. Using causal discovery algorithms, we show that classical suppressors defined by Horst (1941) are generated from causal structures which reveal the equivalence between suppressors and instrumental variables. Although the educational and psychological measurement literature has long recommended that researchers include suppressors in regression models, the causal inference literature has recently recommended that researchers exclude instrumental variables. The conflicting views between the two disciplines can be resolved by considering the different purposes of statistical models, prediction and causal explanation.

scholarly journals Analysing causal structures with entropy

2017 ◽  
Vol 473 (2207) ◽  
pp. 20170483 ◽  
Author(s):  
Mirjam Weilenmann ◽  
Roger Colbeck
Keyword(s):  
Causal Inference ◽  
Quantum Cryptography ◽  
Decision Problem ◽  
Causal Structure ◽  
Central Question ◽  
Open Problems ◽  
Classical Quantum ◽  
The Difference ◽  
Key Aspects ◽  
Causal Structures

A central question for causal inference is to decide whether a set of correlations fits a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for certificates of compatibility. Here, we review several such approaches based on entropy. We bring together the key aspects of these entropic techniques with unified terminology, filling several gaps and establishing new connections, all illustrated with examples. We consider cases where unobserved causes are classical, quantum and post-quantum, and discuss what entropic analyses tell us about the difference. This difference has applications to quantum cryptography, where it can be crucial to eliminate the possibility of classical causes. We discuss the achievements and limitations of the entropic approach in comparison to other techniques and point out the main open problems.

scholarly journals Beyond Causal Explanation: Einstein’s Principle Not Reichenbach’s

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 114
Author(s):  
Michael Silberstein ◽  
William Mark Stuckey ◽  
Timothy McDevitt
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Causal Explanation ◽  
Causal Structure ◽  
Minkowski Spacetime ◽  
Physical Principle ◽  
Causal Principle ◽  
Complete Rejection ◽  
Epr Correlations ◽  
Tsirelson Bound

Our account provides a local, realist and fully non-causal principle explanation for EPR correlations, contextuality, no-signalling, and the Tsirelson bound. Indeed, the account herein is fully consistent with the causal structure of Minkowski spacetime. We argue that retrocausal accounts of quantum mechanics are problematic precisely because they do not fully transcend the assumption that causal or constructive explanation must always be fundamental. Unlike retrocausal accounts, our principle explanation is a complete rejection of Reichenbach’s Principle. Furthermore, we will argue that the basis for our principle account of quantum mechanics is the physical principle sought by quantum information theorists for their reconstructions of quantum mechanics. Finally, we explain why our account is both fully realist and psi-epistemic.

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.

scholarly journals Is coding a relevant metaphor for the brain?

2018 ◽  
Vol 42 ◽  
Author(s):  
Romain Brette
Keyword(s):  
Brain Function ◽  
Neural Coding ◽  
Causal Structure ◽  
Linear Chain ◽  
Neural Codes ◽  
Experimental Parameters ◽  
Representational Power ◽  
Causal Structures ◽  
Perceptual Systems ◽  
The Brain

Abstract “Neural coding” is a popular metaphor in neuroscience, where objective properties of the world are communicated to the brain in the form of spikes. Here I argue that this metaphor is often inappropriate and misleading. First, when neurons are said to encode experimental parameters, the neural code depends on experimental details that are not carried by the coding variable (e.g., the spike count). Thus, the representational power of neural codes is much more limited than generally implied. Second, neural codes carry information only by reference to things with known meaning. In contrast, perceptual systems must build information from relations between sensory signals and actions, forming an internal model. Neural codes are inadequate for this purpose because they are unstructured and therefore unable to represent relations. Third, coding variables are observables tied to the temporality of experiments, whereas spikes are timed actions that mediate coupling in a distributed dynamical system. The coding metaphor tries to fit the dynamic, circular, and distributed causal structure of the brain into a linear chain of transformations between observables, but the two causal structures are incongruent. I conclude that the neural coding metaphor cannot provide a valid basis for theories of brain function, because it is incompatible with both the causal structure of the brain and the representational requirements of cognition.

scholarly journals Theoretical framework for higher-order quantum theory

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180706 ◽  
Author(s):  
Alessandro Bisio ◽  
Paolo Perinotti
Keyword(s):  
Quantum Theory ◽  
Convex Sets ◽  
Mathematical Structure ◽  
Higher Order ◽  
Equivalence Relations ◽  
Full Generality ◽  
Special Cases ◽  
Different Types ◽  
Causal Structures

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes recursively, with the construction of a full hierarchy of maps of increasingly higher order. The analysis of special cases already showed that higher-order quantum functions exhibit features that cannot be tracked down to the usual circuits, such as indefinite causal structures, providing provable advantages over circuital maps. The present treatment provides a general framework where this kind of analysis can be carried out in full generality. The hierarchy of higher-order quantum maps is introduced axiomatically with a formulation based on the language of types of transformations. Complete positivity of higher-order maps is derived from the general admissibility conditions instead of being postulated as in previous approaches. The recursive characterization of convex sets of maps of a given type is used to prove equivalence relations between different types. The axioms of the framework do not refer to the specific mathematical structure of quantum theory, and can therefore be exported in the context of any operational probabilistic theory.

On Quantum Capacity and its Bound

2003 ◽  
Vol 06 (02) ◽  
pp. 301-310 ◽  
Author(s):  
Masanori Ohya ◽  
Igor V. Volovich
Keyword(s):  
Quantum Channel ◽  
Quantum Mechanical ◽  
Quantum Capacity ◽  
Classical Quantum ◽  
Mutual Entropy

The quantum capacity of a pure quantum channel and that of classical-quantum-classical channel are discussed in detail based on the fully quantum mechanical mutual entropy. It is proved that the quantum capacity generalizes the so-called Holevo bound.

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