Related papers: Numerical studies of entangled PPT states in compo…
Using a geometric measure of entanglement quantification based on Euclidean distance of the Hermitian matrices, we obtain the minimum distance between a bipartite bound entangled $n$- qudit density matrix and the maximally mixed state.This…
We experimentally generate and tomographically characterize a mixed, genuinely non-Gaussian bipartite continuous-variable entangled state. By testing entanglement in 2$\times$2-dimensional two-qubit subspaces, entangled qubits are localized…
Numerical approximation of quantum states via convex combinations of states with positive partial transposes (bi-PPT state) in multipartite systems constitutes a fundamental challenge in quantum information science. We reformulate this…
An algebraic procedure to find extremal density matrices for any Hamiltonian of a qudit system is established. The extremal density matrices for pure states provide a complete description of the system, that is, the energy spectra of the…
We present a construction of new bound entangled states from given bound entangled states for arbitrary dimensional bipartite systems. One way to construct bound entangled states is to show that these states are PPT (positive partial…
We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map Phi which operates on state spaces with even dimension N >= 4. It is shown that Phi detects many entangled states…
We present the modified relative entropy of entanglement for multi-party systems by a given relative density matrix which is spanned by a linear combination of the direct products of so-called basis of relative density matrices and reduced…
In this paper, we consider a system of homogeneous algebraic equations in complex variables and their conjugates, which arise naturally from the range criterion for separability of PPT states. We examine systematically these equations to…
The convex set of quantum states of a composite $K \times K$ system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an…
Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information…
We investigate conditions on a finite set of multi-partite product vectors for which separable states with corresponding product states have unique decomposition, and show that this is true in most cases if the number of product vectors is…
We theoretically derive the probability densities of the entanglement measures of a pure non-ergodic many-body state, represented in a bipartite product basis and with its reduced density matrix described by a generalized, multi-parametric…
The existence of a maximally entangled pure state is a cornerstone result of entanglement theory that has paramount consequences in quantum information theory. A natural generalization of this property is to consider whether a notion of…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
The entanglement content of superpositions of quantum states is investigated based on a measure called {\it concurrence}. Given a bipartite pure state in arbitrary dimension written as the quantum superposition of two other such states, we…
These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular…
Entanglement distillation is a key task in quantum-information processing. In this paper, we distill non-positive-partial-transpose (NPT) bipartite states of some given Schmidt rank and matrix rank. We show that all bipartite states of…
Using the monotonity of relative entropy of composite quantum systems we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Example of qutrit state inequalities and the "qubit portrait" bound for the…
In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space…
We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite…