Related papers: Conditional quantization for uniform distributions…
The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce $\textit{collective}$ randomized…
We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We…
We survey results on the distribution of zeros of random polynomials and of random holomorphic sections of line bundles, especially for large classes of probability measures on the spaces of holomorphic sections. We provide furthermore some…
The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…
The Bessel point process is a rigid point process on the positive real line and its conditional measure on a bounded interval $[0,R]$ is almost surely an orthogonal polynomial ensemble. In this article, we show that if $R$ tends to…
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…
We establish an equidistribution theorem for the common zeros of random sections of high powers of several singular Hermitian big line bundles associated to moderate measures.
Quantile regression models provide a wide picture of the conditional distributions of the response variable by capturing the effect of the covariates at different quantile levels. In most applications, the parametric form of those…
Majorization provides a rather powerful partial-order classification of probability distributions depending only on the spread of the statistics, and not on the actual numerical values of the variable being described. We propose to apply…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
Various categories have been proposed as targets for the denotational semantics of higher-order probabilistic programming languages. One such proposal involves joint probability distributions (couplings) used in Bayesian statistical models…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in…
We use the canonical coset parameterization and provide a formula with the unitary part of the Bures measure for non-degenerate systems in terms of the product of even Euclidean balls. This formula is shown to be consistent with the…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…
To begin with, it is pointed out that the form of the quantum probabil- ity formula originates in the very initial state of the object system as seen when the state is expanded with the eigen-projectors of the measured ob- servable. Making…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
The main result of this paper is that conditional measures of generalized Ginibre point processes, with respect to the configuration in the complement of a bounded open subset on $\mathbb{C}$, are orthogonal polynomial ensembles with…
There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability…
In this paper, the quantization dimensions of the Borel probability measures supported on the limit sets of the bi-Lipschitz recurrent iterated function systems under the strong open set condition in terms of the spectral radius have been…