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In the present paper the cross norm criterion for separability of density matrices is studied. In the first part of the paper we determine the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal…
Universal two-particle entanglement processes are analyzed in arbitrary dimensional Hilbert spaces. On the basis of this analysis the class of possible optimal universal entanglement processes is determined whose resulting output states do…
Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case…
We propose an algorithm which proves a given bipartite quantum state to be separable in a finite number of steps. Our approach is based on the search for a decomposition via a countable subset of product states, which is dense within all…
We present a necessary and sufficient condition for the separability of multipartite quantum states, this criterion also tells us how to write a multipartite separable state as a convex sum of separable pure states. To work out this…
We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow to detect the entanglement…
We propose a sufficient and necessary separability criterion for pure states in multipartite and high dimensional systems. Its main advantage is operational and computable. The obvious expressions of this criterion can be given out by the…
Many important sets of normalized states in a multipartite quantum system of finite dimension d, such as the set S of all separable states, are real semialgebraic sets. We compute dimensions of many such sets in several low-dimensional…
A pure multipartite quantum state is called absolutely maximally entangled (AME), if all reductions obtained by tracing out at least half of its parties are maximally mixed. Maximal entanglement is then present across every bipartition. The…
Based on the realignment moments of density matrix, we study parameterized entanglement criteria for bipartite and multipartite states. By adjusting the different parameter values, our criterion can detect not only bound entangled states,…
Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum…
The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices,…
We present here an overview of our work concerning entanglement properties of composite quantum systems. The characterization of entanglement, i.e. the possibility to assert if a given quantum state is entangled with others and how much…
The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for…
To determine whether a given multipartite quantum state is separable with respect to some partition we construct a family of entanglement measures R_m. This is done utilizing generalized concurrences as building blocks which are defined by…
Recent findings suggest, separable states, which are otherwise of no use in entanglement dependent tasks, can also be used in information processing tasks that depend upon the discord type general non classical correlations. In this work,…
Quantum entanglement between several particles is essential for applications like quantum metrology or quantum cryptography, but it is also central for foundational phenomena like quantum non-locality. This leads to the problem of…
We give necessary conditions for the mixing problem in bipartite case, which are independent of eigenvalues and based on algebraic-geometric invariants of the bipartite states. One implication of our results is that for some special…
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…
Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki…