Related papers: A Concise Formula for Generalized Two-Qubit Hilber…

We give a deterministic method of quasi-polynomial complexity to approximate the volume of the intersection of the unit hypercube with two specific sets. The method can actually be applied (without losing the quasi-polynomial complexity) to…

We study the probability that a random polynomial with integer coefficients is reducible when factored over the rational numbers. Using computer-generated data, we investigate a number of different models, including both monic and non-monic…

Let $X$ be a Bernoulli random variable with the success probability $p$. We are interested in tight bounds on $\mathbb{E}[f(X_1,X_2)]$, where $X_i=\mathbb{E}[X| \mathcal{F}_i]$ and $\mathcal{F}_i$ are some sigma-algebras. This problem is…

Let $\D$ be a set of $n$ pairwise disjoint unit balls in $\R^d$ and $P$ the set of their center points. A hyperplane $\Hy$ is an \emph{$m$-separator} for $\D$ if each closed halfspace bounded by $\Hy$ contains at least $m$ points from $P$.…

Let $f(z)={}_nF_{n-1}(\mathbf{\alpha},\mathbf{\beta})$ be the hypergeometric series with parameters $\mathbf{\alpha} = (\alpha_1,\ldots,\alpha_n)$ and $\mathbf{\beta} = (\beta_1,\ldots,\beta_{n-1},1)$ in $(\mathbb{Q}\cap(0,1])^n$, let…

The fidelity susceptibility serves as a universal probe for quantum phase transitions, offering an order-parameter-free metric that captures ground-state sensitivity to Hamiltonian perturbations and exhibits critical scaling. Classical…

In this paper, we consider an infinite dimensional exponential family, $\mathcal{P}$ of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, $H$ and show it to be quite rich in the sense that a…

We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…

Two-term asymptotic formulae for the probability distribution functions for the smallest eigenvalue of the Jacobi $ \beta $-Ensembles are derived for matrices of large size in the r\'egime where $ \beta > 0 $ is arbitrary and one of the…

A new necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The new…

An approach to build Probabilistic Arithmetic in which initial values of all correlated random variables are known, but with varying degrees of accuracy. As a result of the proposed Probabilistic Arithmetic operations, variable values,…

The main aim of this work is to derive the $q$-recurrence relations, $q$-partial derivative relations and summation formula of bibasic Humbert hypergeometric function $\Phi_1$ on two independent bases $q$ and $q_{1}$ of two variables and…

We pursue a number of analytical directions, motivated to some extent initially by the possibility of developing a methodology for formally proving or disproving a certain conjecture of quantum-theoretical relevance (quant-ph/0308037). It…

In this work, we use probability groups, introduced by Harrison in 1979, as a tool to study a semisimple Hopf algebra $H$ with a commutative character ring and prove that the algebra generalized by the dual probability group is the center…

We first find an explicit formula for the square root of positive $2 \times 2$ operator matrices with commuting entries, and then use it to define and study semi-hyponormality for commuting pairs of Hilbert space operators. \ For the…

In continuation of our previous works J. Phys. A: Math. Gen. 35, 9355-9365 (2002), J. Phys. A: Math. Gen. 38, 7851 (2005) and Eur. Phys. J. D 72, 172 (2018), we investigate a class of generalized coherent states for associated Jacobi…

Let A and B be two connected graded commutative k-algebras of finite type, where k is a perfect field of positive characteristic p. We prove that the quasi--shuffle algebras generated by A and B are isomorphic as Hopf algebras if and only…

We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method provides rigorous…

Study of an N qubit mixed symmetric separable states is a long standing challenging problem as there exist no unique separability criterion. In this regard, we take up the N-qubit mixed symmetric separable states for a detailed study as…

A proof that minimum uncertainty states of the simplest periodic quantum system exist in a state space that is represented by a Colombeau algebra of generalised functions but not in Hilbert space or in the space of Schwartz distributions is…