Related papers: Multiple-event probability in general-relativistic…
In quantum theory, the modulus-square of the inner product of two normalized Hilbert space elements is to be interpreted as the transition probability between the pure states represented by these elements. A probabilistically motivated and…
We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
Non-commutative spacetime and quantum groups have been argued to capture non-classical features of spacetime and its symmetries in the low-energy limit of quantum gravity. In this letter, we show that employing the $SU_q(2)$ quantum group…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
We define a simple rule that allows to describe sequences of projective measurements for a broad class of generalized probabilistic models. This class embraces quantum mechanics and classical probability theory, but, for example, also the…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
Transition probabilities are an important and useful tool in quantum mechanics. However, in their present form, they are limited in scope and only apply to pure quantum states. In this article we extend their applicability to mixed states…
I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite…
There are two different and logically independent concepts of noncontextuality in quantum mechanics. First, an ontological (hidden variable) model for quantum mechanics is called noncontextual if every ontic (hidden) state determines the…
In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…
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…
Certain concrete "ontological models" for quantum mechanics (models in which measurement outcomes are deterministic and quantum states are equivalent to classical probability distributions over some space of `hidden variables') are…
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…
Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…
Concept of entangled probability distribution of several random variables is introduced. These probability distributions describe multimode quantum states in probability representation of quantum mechanics. Example of entangled probability…