Related papers: Eigenvalues, Peres' separability condition and ent…
Hermitian tensors are natural generalizations of Hermitian matrices, while possessing rather different properties. A Hermitian tensor is separable if it has a Hermitian decomposition with only positive coefficients, i.e., it is a sum of…
We derive a collection of separability conditions for bipartite systems of dimensions d X d which is based on the entropic version of the uncertainty relations. A detailed analysis of the two-qubit case is given by comparing the new…
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 explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial…
We discuss the relationship between entropic uncertainty relations and entanglement. We present two methods for deriving separability criteria in terms of entropic uncertainty relations. Especially we show how any entropic uncertainty…
We explain several separability criteria which rely on uncertainty relations. For the derivation of these criteria uncertainty relations in terms of variances or entropies can be used. We investigate the strength of the separability…
We consider those Gaussian Unitary Ensembles where the eigenvalues have prescribed multiplicities, and obtain joint probability density for the eigenvalues. In the simplest case where there is only one multiple eigenvalue t, this leads to…
A quantum system consisting of two subsystems is separable if its density matrix can be written as $\rho=\sum w_K \rho_K'\otimes \rho_K''$, where $\rho_K'$ and $\rho_K''$ are density matrices for the two subsytems, and the positive weights…
We study separability criteria in multipartite quantum systems of arbitrary dimensions by using the Bloch representation of density matrices. We first derive the norms of the correlation tensors and obtain the necessary conditions for…
We investigate the entanglement properties of multiparticle systems, concentrating on the case where the entanglement is robust against disposal of particles. Two qubits -belonging to a multipartite system- are entangled in this sense iff…
We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product is separable or entangled. We show that the tensor convolution defined for certain mappings on an almost arbitrary…
With a probability of success of $95 \%$ we solve the separability problem for Bell diagonal qutrit states with positive partial transposition (PPT). The separability problem, i.e. distinguishing separable and entangled states, generally…
This note presents explicit formulae for the exponentials of a wide variety of matrices which are 4x4, anti-Hermitian. Easily verifiable conditions characterizing when such matrices admit one of three minimal polynomials are also given.…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
We propose one and a half criteria for determining how many measurements are needed to quantify entanglement reliably. We base these criteria on Bayesian analysis of measurement results, and apply our methods to four-qubit entanglement, but…
We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
We propose novel mixed states in two qubits, ``maximally entangled mixed states'', which have a property that the amount of entanglement of these states cannot be increased further by applying any unitary operations. The property is proven…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…