Related papers: Generalized Fock space and contextuality
Identifying when observed statistics cannot be explained by any reasonable classical model is a central problem in quantum foundations. A principled and universally applicable approach to defining and identifying nonclassicality is given by…
Quantum theory is a probabilistic theory with fixed causal structure. General relativity is a deterministic theory but where the causal structure is dynamic. It is reasonable to expect that quantum gravity will be a probabilistic theory…
This paper provides a bundle perspective to contextuality by introducing new categories of contextuality scenarios based on bundles of simplicial complexes and simplicial sets. The former approach generalizes earlier work on the…
We analyze different aspects of our quantum modeling approach of human concepts, and more specifically focus on the quantum effects of contextuality, interference, entanglement and emergence, illustrating how each of them makes its…
It is useful to have a criterion for when the predictions of an operational theory should be considered classically explainable. Here we take the criterion to be that the theory admits of a generalized-noncontextual ontological model.…
In this paper we develop an operational formulation of General Relativity similar in spirit to existing operational formulations of Quantum Theory. To do this we introduce an operational space (or op-space) built out of scalar fields. A…
Models of a phenomenon are often developed by examining it under different experimental conditions, or measurement contexts. The resultant probabilistic models assume that the underlying random variables, which define a measurable set of…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of…
A family of probability distributions attached to a class of generalized weighted Bergman spaces on the Poincar\'e disk are introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained…
We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…
Contextuality and nonlocality are non-classical properties exhibited by quantum statistics whose implications profoundly impact both foundations and applications of quantum theory. In this paper we provide some insights into logical…
Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the…
Causal inference is a key research area in machine learning, yet confusion reigns over the tools needed to tackle it. There are prevalent claims in the machine learning literature that you need a bespoke causal framework or notation to…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of…
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…
There exist several phenomena (systems) breaking the classical probability laws. Such systems are contextual dependent adaptive systems. In this paper, we present a new mathematical formula to compute the probability in those systems by…
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…