Related papers: A Geometric Diagram of Separable States
For a given Hamiltonian $H$ on a multipartite quantum system, one is interested in finding the energy $E_0$ of its ground state. In the separability approximation, arising as a natural consequence of measurement in a separable basis, one…
The set of all separable quantum states is compact and convex. We focus on the two-qubit quanum system and study the boundary of the set. Then we give the criterion to determine whether a separable state is on the boundary. Some…
Let H[N] denote the tensor product of n finite dimensional Hilbert spaces H(r). A state |phi> of H[N] is separable if |phi> is the tensor product of states in the respective product spaces. An orthogonal unextendible product basis is a…
The computable measure of the mixed-state entanglement, the negativity, is shown to admit a clear geometrical interpretation, when applied to Schmidt-correlated (SC) states: the negativity of a SC state equals a distance of the state from a…
In this paper, we show that an arbitrary separable state can be the output of a certain entanglement-breaking channel corresponding exactly to the input of a maximally entangled state. A necessary and sufficient separability criterion and…
We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of $n\times n$ bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable…
We introduce a new family of separability criteria that are based on the existence of extensions of a bipartite quantum state $\rho$ to a larger number of parties satisfying certain symmetry properties. It can be easily shown that all…
The geometric measure of entanglement (GME) quantifies how close a multi-partite quantum state is to the set of separable states under the Hilbert-Schmidt inner product. The GME can be non-multiplicative, meaning that the closest product…
We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure…
We give a criterion for a positive mapping on the space of operators on a Hilbert space to be indecomposable. We show that this criterion can be applied to two families of positive maps. These families of maps can then be used to form…
In this paper, we give out some effective criterions which can be used to judge the separability of multipartite pure states. We obtain the relationship between separability and Schmidt decomposable of multipartite pure states in Theorem1.…
Employing a recently proposed separability criterion we develop analytical lower bounds for the concurrence and for the entanglement of formation of bipartite quantum systems. The separability criterion is based on a nondecomposable…
By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix $\rho$ and the vectorization of its reduced density matrices, we present a family of separability criteria, which are stronger than the…
Explicit sufficient and necessary conditions for separability of $N$-dimensional rank two multiparty quantum mixed states are presented. A nonseparability inequality is also given, for the case where one of the eigenvectors corresponding to…
Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
We present a criterion of separability for arbitrary s partitions of N-particle fermionic pure states. We show that, despite the superficial non-factorizability due to the antisymmetry required by the indistinguishability of the particles,…
In this paper, we consider a subclass of quantum states in the multipartite system, namely, the supersymmetric states. We investigate the problem whether they admit the symmetrically separable decomposition, i.e., each term in this…
We construct a density matrix whose elements are written in terms of expectation values of non-Hermitian operators and their products for arbitrary dimensional bipartite states. We then show that any expression which involves matrix…
A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. Every symmetric operator, represented by a symmetric matrix with only two nonzero elements, and their…