Related papers: Characteristic function and operator approach to M…
In this paper we will turn our attention to the problem of obtaining phase-space probability density functions. We will show that it is possible to obtain functions which assume only positive values over all its domain of definition.
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…
A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
In this Letter, we interpret the Husimi function as the conditional probability density of continuously measuring a stream of constant position and momentum outcomes, indefinitely. This gives rise to an alternative definition that naturally…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
In this paper, we look at a probabilistic approach to a non-local quadratic form that has lately attracted some interest. This form is related to a recently introduced non-local normal derivative. The goal is to construct two Markov…
Previously, the author offered a plasma-like description of quantum phenomena. This article offers a new criterion of approximation of probability density functions of quantum theories by sums of $\delta$-functions with integer coefficients…
We propose an unexplored quantization method. It is based on the assumption of dynamical space-time intrinsic periodicities for relativistic fields, which in turn can be regarded as dual to extra-dimensional fields. As a consequence we…
In quantum operations, probabilities characterise both the degree of the success of a state transformation and, as density operator eigenvalues, the degree of mixedness of the final state. We give a unified treatment of pure-to-pure state…
It is widely believed that statistical interpretation of quantum mechanics requires that density operators representing quantum states be normalized. We present a description of selective measurements in terms of density operators. The…
We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of…
We describe the representation of arbitrary density operators in terms of expectation values of simple projection operators. Two representations are presented which yield non--recursive schemes for experimentally determining the density…
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…
A two-level atom interacting with an electromagnetic mode in a cavity experiences population collapses and revivals. They are an indirect signature of the field quantization, and also hold information about the mode. Thus, they may be…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
This paper presents a general method for producing randomly perturbed density operators subject to different sets of constraints. The perturbed density operators are a specified "distance" away from the state described by the original…
We give here a constructive account of the frequentist approach to probability, by means of natural density. Using this notion of natural density, we introduce some probabilistic versions of the Limited Principle of Omniscience. Finally we…