Related papers: The quantum separability problem is a simultaneous…
We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our…
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility…
We study the concepts of compatibility and separability and their implications for quantum and classical systems. These concepts are illustrated on a macroscopic model for the singlet state of a quantum system of two entangled spin 1/2 with…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous…
We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria for identifying entangled states and…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed…
The paper describes a solution to the problem of quantum measurement that has been proposed recently. The literal understanding of the basic rule of quantum mechanics on identical particles violates the cluster separation principle and so…
After introducing the partially separable concept, we proved the equivalence between the partial separability of a given $m$-partite subsystem with $m$ qubits and the purity of states of this $m$-partite subsystem for a pure state in…
The concurrence, a quantitative measure of the entanglement between a pair of particles, is determined for the case where the pair is extracted from a symmetric state of N two-level systems. Examples are given for both pure and mixed states…
We study generalized concurrences as a tool to detect the entanglement of bipartite quantum systems. By considering the case of 2 X 4 states of rank 2, we prove that generalized concurrences do not, in general, give a necessary and…
Covariance matrices are a useful tool to investigate correlations and entanglement in quantum systems. They are widely used in continuous variable systems, but recently also for finite dimensional systems powerful entanglement criteria in…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we…
The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential…
For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.
We present a general description of separable states in Quantum Mechanics. In particular, our result gives an easy proof that inseparabitity (or entanglement) is a pure quantum (noncommutative) notion. This implies that distinction between…
The absolute separability problem asks for a characterization of the quantum states $\rho \in M_m\otimes M_n$ with the property that $U\rho U^\dagger$ is separable for all unitary matrices $U$. We investigate whether or not it is the case…