Related papers: Effective criteria for entanglement witnesses in s…
We use operators from generalized equiangular measurements to construct positive maps. Their positivity follows from the inequality for indices of coincidence corresponding to few equiangular tight frames. These maps give rise to…
We transform the way of finding entanglement criterion into two steps: to obtain necessary criterion of separability by maximizing an algebra function for a set of characteristic variables of the witness operator and the given number of…
Motivated by the Peres-Horodecki criterion and the realignment criterion we develop a more powerful method to identify entangled states for any bipartite system through a universal construction of the witness operator. The method also gives…
We provide a class of optimal nondecomposable entanglement witnesses for 4N x 4N composite quantum systems or, equivalently, a new construction of nondecomposable positive maps in the algebra of 4N x 4N complex matrices. This construction…
Certifying entanglement of a multipartite state is generally considered as a demanding task. Since an $N$ qubit state is parametrized by $4^{N}-1$ real numbers, one might naively expect that the measurement effort of generic entanglement…
We present a survey on mathematical topics relating to separable states and entanglement witnesses. The convex cone duality between separable states and entanglement witnesses is discussed and later generalized to other families of…
We provide a new class of indecomposable entanglement witnesses. In 4 x 4 case it reproduces the well know Breuer-Hall witness. We prove that these new witnesses are optimal and atomic, i.e. they are able to detect the "weakest" quantum…
If one wants to establish optimality of a given bipartite entanglement witness, the current standard approach is to check whether it has the spanning property. Although this is not necessary for optimality, it is most often satisfied in…
We present an intuitive geometrical entanglement criterion. It allows formulation of simple and experimentally friendly sufficient conditions for entanglement. The conditions are illustrated with several examples. Moreover, a generalization…
From the physical point of view entanglement witnesses define a universal tool for analysis and classification of quantum entangled states. From the mathematical point of view they provide highly nontrivial generalization of positive…
It is well known that the support of an optimal decomposable entanglement witness is completely entangled. We add two more necessary conditions for the optimality: The orthogonal complement of the support must have a nonzero product vector;…
We establish an explicit criterion for determining whether a $4 \times 4$ upper-triangular matrix is a contraction with respect to the Euclidean operator norm.
Entanglement detection problem is one of the important problem in quantum information theory. Gurvit showed that this problem is NP complete and thus this may be the possible reason that only one criterion is not sufficient to detect all…
We interpret multi-partite genuine entanglement witnesses as simultaneous positivity of various maps arising from them. We apply this result to multi-qubit {\sf X}-shaped Hermitian matrices, and characterize the conditions for them to be…
Entanglement witnesses are observables which when measured, detect entanglement in a measured composed system. It is shown what kind of relations between eigenvectors of an observable should be fulfilled, to allow an observable to be an…
We introduce informationally complete measurements whose outcomes are entanglement witnesses and so answer the question of how many witnesses need to be measured to decide whether an arbitrary state is entangled or not: as many as the…
We link the study of positive quantum maps, block positive operators, and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block positive operators relate to biquadratic…
We investigate how stabilizer theory can be used for constructing sufficient conditions for entanglement. First, we show how entanglement witnesses can be derived for a given state, provided some stabilizing operators of the state are…
We present a multi-parameter family of positive maps between spaces of differing dimensions. This framework facilitates the construction of Entanglement Witnesses (EWs) specifically designed for systems living in $d_1 \times d_2$…
We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values of Hermitian operators…