Related papers: Quantum Informatics View of Statistical Data Proce…
We study quantum tomography from a continuous measurement record obtained by measuring expectation values of a set of Hermitian operators obtained from unitary evolution of an initial observable. For this purpose, we consider the…
We give here a semi-analytic formula for the density of critical values for chi random fields on a general manifold. The result uses Kac-Rice argument and a convenient representation for the Hessian matrix of chi fields, which makes the…
In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as…
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the…
This text provides a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous…
Based on operator algebras commonly used in quantum mechanics some properties of special functions such as Hermite and Laguerre polynomials and Bessel functions are derived.
Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
There is an intense and partly recent literature focussing on the problem of selecting the bandwidth parameter for kernel density estimators. Available methods are largely `very nonparametric', in the sense of not requiring any knowledge…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high…
Partitions of the set of primes are introduced based on the Chebyshev polynomials at rationals. The prime densities of all such partitions are established. Euler's Criterion for $SL(2,\mathbb Q)$ is formulated, which is the bridge between…
We propose a model for computing of a certain set of analytical functions based on estimating the output distribution of multiphoton outcomes in an optical scheme with an initial single-mode squeezed vacuum (SMSV) state and photonic states…
Particle distributions in squeezed states, even and odd coherent states are given in terms of multivariable Hermite polynomials. The Q--function and Wigner function for nonclassical field states are discussed.
Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the…
Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the…
We give expansions of reproducing kernels of the Christoffel-Darboux type in terms of Schur polynomials. For this, we use evaluations of averages of characteristic polynomials and Schur polynomials in random matrix ensembles. We explicitly…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
The random matrix ensembles (RMT) of quantum statistical Hamiltonian operators, e.g.Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…