Related papers: Determination of the Schmidt number
We prove a lower bound for Schmidt numbers of bipartite mixed states. This lower bound can be applied easily to low rank bipartite mixed states. From this lower bound it is known that generic low rank bipartite mixed states have relatively…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
A two-step optimization is proposed to represent an arbitrary quantum state to a desired accuracy with the least number of gaussians in phase space. The Husimi distribution of the quantum state provides the information to determine the…
Using the necessary and sufficient conditions, minimum error discrimination among two sets of similarity transformed equiprobable quantum qudit states is investigated. In the case that the unitary operators are generating sets of two…
We propose a generalized discrimination scheme for mixed quantum states. In the present scenario we allow for certain fixed fraction of inconclusive results and we maximize the success rate of the quantum-state discrimination. This protocol…
By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in…
We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we…
We introduce the notion of a Schmidt number of a bipartite density matrix, characterizing the minimum Schmidt rank of the pure states that are needed to construct the density matrix. We prove that Schmidt number is nonincreasing under local…
We apply the generalised concept of witness operators to arbitrary convex sets, and review the criteria for the optimisation of these general witnesses. We then define an embedding of state vectors and operators into a higher-dimensional…
In this work we estimate the transverse Schmidt number for the bipartite bright squeezed vacuum state by means of second-order intensity correlation function measurement. Assuming that the number of modes is equal in both beams we determine…
Optimized Schwarz Methods (OSMs) are based on optimized transmission conditions along the interfaces between the subdomains. Optimized transmission conditions are derived at the theoretical level, using techniques developed in the last…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical…
We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…
The phase estimation algorithm is so named because it allows the estimation of the eigenvalues associated with an operator. However it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this…
In [1] Zhu and Rabitz presented a rapidly convergent iterative algorithm for optimal control of the expectation value of a positive definite observable in a pure-state quantum system. In this paper we generalize this algorithm to a quantum…
We consider the Schrodinger operator a given domain. Our goal is to study some optimization problems where an optimal (non-negative) potential V has to be determined in some suitable admissible classes and for some suitable optimization…
In this study the determinant of the average quadratic error matrix is used as the measure of state estimation efficiency. This quantity is easily computable in some cases, so it gives us a reasonable tool to find optimal measurement setup…
We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…
Numerical range of a Hermitian operator X is defined as the set of all possible expectation values of this observable among a normalized quantum state. We analyze a modification of this definition in which the expectation value is taken…