Related papers: Probability density of quantum expectation values
A distribution of electromagnetic fields presents a statistical assembly of a particular type, which is at scale h a quantum statistical assembly itself and has also been instrumental to concretisation of the basic probability assumption of…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
We consider the problem of estimating the density $\Pi$ of a determinantal process $N$ from the observation of $n$ independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish…
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…
I explore the possibility that a quantum system S may be described completely by the combination of its standard quantum state $|\psi\rangle$ and a (hidden) quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that the…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
We present a universal technique for quantum state estimation based on the maximum-likelihood method. This approach provides a positive definite estimate for the density matrix from a sequence of measurements performed on identically…
A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, $\rho = \sum_i p_i |\psi_i\ra \la \psi_i|$. This paper characterizes the class of probability distributions $(p_i)$ that may appear in such a…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…
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…
The Hellinger distance between quantum states is a significant measure in quantum information theory, known for its Riemannian and monotonic properties. It is also easier to compute than the Bures distance, another measure that shares these…
Ensembles of random density matrices determined by various probability measures are analysed. A simple and efficient algorithm to generate at random density matrices distributed according to the Bures measure is proposed. This procedure may…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or…