Related papers: Imprecise probability for non-commuting observable…

We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases…

Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…

The principle of complementarity is quantified in two ways: by a universal uncertainty relation valid for arbitrary joint estimates of any two observables from a given measurement setup, and by a general uncertainty relation valid for…

The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…

We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…

We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…

In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other matrix quantities. Those quantities might be the diagonal…

Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…

Most of the fundamental characteristics of quantum mechanics, such as non-locality and contextuality, are manifest in discrete, finite-dimensional systems. However, many quantum information tasks that exploit these properties cannot be…

The problem as to when two noncommuting observables are considered to have the same value arises commonly, but shows a nontrivial difficulty. Here, an answer is given by establishing the notion of perfect correlations between noncommuting…

It is well-established that quantum probability does not follow classical Kolmogorov probability calculus. Various approaches have been developed to loosen the axioms, of which the use of signed measures is the most successful (e.g. the…

We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…

As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…

A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…

A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…

The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes…

In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the…

A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…

We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…

We show that the probabilistic distribution over the space in the spectator world, can be associated via noncommutative geometry (with some modifications) to a metric in which the particle lives. According to this geometrical view, the…