Related papers: General probabilistic theories: An introduction
We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalise the traditional quantum-to-classical transition.…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
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…
Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a…
Generalized contextuality refers to our inability of explaining measurement statistics using a context-independent probabilistic and ontological model. On the other hand, measurement statistics can also be modeled using the framework of…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
We give an introductory account of the general boundary formulation of quantum theory. We refine its probability interpretation and emphasize a conceptual and historical perspective. We give motivations from quantum gravity and illustrate…
The generalized number-theoretic transformation (NPT) is formulated on the basis of the exponential function theorem, which allows us to replace operations modulo the expression as a whole by modulo operations on the exponent of this…
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 text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
In this paper I give overviews of the polysymplectic approach to covariant Hamiltonian field theory and the simplest geometric quantization of classical particle theories. I then give a synopsis of a recently proposed toy model for applying…
It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understanding of the probabilistic or information theoretic foundations…
What singles out quantum mechanics as the fundamental theory of Nature? Here we study local measurements in generalised probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We…
There exist several simple representations of uncertainty that are easier to handle than more general ones. Among them are random sets, possibility distributions, probability intervals, and more recently Ferson's p-boxes and Neumaier's…
This paper presents in detail the generalized pignistic transformation (GPT) succinctly developed in the Dezert-Smarandache Theory (DSmT) framework as a tool for decision process. The GPT allows to provide a subjective probability measure…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
Causality is one of the most fundamental notions in physics. Generalized probabilistic theories (GPTs) and the process matrix framework incorporate it in different forms. However, a direct connection between these frameworks remains…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
An introductory to generalized parton distributions is given which emphasizes their spectral property and its uses as well as the equivalence of various GPD representations. Furthermore, the status of the theory and phenomenology of hard…