Related papers: Sufficient separability criteria and linear maps

Mutually unbiased measurements (MUMs) are generalized from the concept of mutually unbiased bases (MUBs) and include the complete set of MUBs as a special case, but they are superior to MUBs as they do not need to be rank one projectors. We…

I consider deterministic distinguishability of a set of orthogonal, bipartite states when only a single copy is available and the parties are restricted to local operations and classical communication, but with the additional requirement…

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 have reexamined the moments of positive maps and the criterion based on these moments to detect entanglement. For two qubits, we observed that reduction map is equivalent to partial transpose map as the resulting matrices have the same…

We propose a range criterion which is a sufficient and necessary condition satisfied by two pure states transformable with each other under reversible stochastic local operations assisted with classical communication. We also provide a…

For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of separable (unentangled) matrices around the identity matrix. This implies a simple and…

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…

We analyze exact ground state (GS) separability in general $N$ particle systems with two-site couplings. General necessary and sufficient conditions for full separability, in the form of one and two-site eigenvalue equations, are first…

In this letter we have established the physical character of pure bipartite states with the same amount of entanglement in the same Schmidt rank that either they are local unitarily connected or they are incomparable. There exist infinite…

In this paper, we study the separability of quantum states in bosonic system. Our main tool here is the "separability witnesses", and a connection between "separability witnesses" and a new kind of positivity of matrices--- "Power Positive…

We study $k$-positive linear maps on matrix algebras and address two problems, (i) characterizations of $k$-positivity and (ii) generation of non-decomposable $k$-positive maps. On the characterization side, we derive optimization-based…

We study the quantum separability problem by using general symmetric informationally complete measurements and present a separability criterion for arbitrary dimensional bipartite systems. We show by detailed examples that our criterion is…

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…

Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using…

Schmidt decomposition is a powerful tool in quantum information. While Schmidt decomposition is universal for bipartite states, its not for multipartite states. In this article, we review properties of bipartite Schmidt decompositions and…

Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a class of indecomposable positive maps in the algebra of 2n x 2n complex matrices with n>1. It is shown that these maps are exposed and hence…

The necessary and sufficient condition of separability of a mixed state of any systems is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled…

A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice (A) and Bob (B), may be more disordered locally than globally. That is, S(A) > S(A,B), where S(.) is the von Neumann entropy. It is known that…

The complete reducibility property for bipartite states reduced the separability problem to a proper subset of positive under partial transpose states and was used to prove several theorems inside and outside entanglement theory. So far…

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…