Related papers: A new class of states with positive partial transp…

We consider rotationally invariant states in $\mathbb{C}^{N_{1}}\ot \mathbb{C}^{N_{2}}$ Hilbert space with even $N_{1}\geq 4$ and arbitrary $N_{2}\geq N_{1}$, and show that in such case there always exist states which are inseparable and…

We study extremality in various sets of states that have positive partial transposes. One of the tools we use for this purpose is the recently formulated criterion allowing to judge if a given state is extremal in the set of PPT states.…

We provide a recurrent construction of entanglement witnesses for a bipartite systems living in a Hilbert space corresponding to $2N$ qubits ($N$ qubits in each subsystem). Our construction provides a new method of generalization of the…

We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear…

We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability…

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…

We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For…

For a system of N identical particles in a random pure state, there is a threshold k_0 = k_0(N) ~ N/5 such that two subsystems of k particles each typically share entanglement if k > k_0, and typically do not share entanglement if k < k_0.…

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…

We introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on…

We provide a generalization of the reduction and Robertson positive maps in matrix algebras. They give rise to a new class of optimal entanglement witnesses. Their structural physical approximation is analyzed. As a byproduct we provide a…

We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…

One of the most fundamental questions in quantum information theory is PPT-entanglement of quantum states, which is an NP-hard problem in general. In this paper, however, we prove that all PPT $(\overline{\pi}_A\otimes \pi_B)$-invariant…

We use some general results regarding positive maps to exhibit examples of non-decomposable maps and 2^N x 2^N, N >= 2, bound entangled states, e.g. non distillable bipartite states of N + N qubits.

We present an alternative approach to unveil a different kind of entanglement in bipartite quantum states whose diagonal zero patterns in suitable matrix representations admit a nice description in terms of triangle-free graphs. Upon…

We prove an analytic positive lower bound for the geometric distance between entangled positive partial transpose (PPT) states of a broad class and any private state that delivers one secure key bit. Our proof holds for any Hilbert space of…

We provide a new class of entanglement witnesses for $d \ot d$ systems (two qudits). Our construction generalizes the one proposed recently by Jafarizadeh et al. for $d=3$ and $d=4$ on the basis of semidefinite linear programming. Moreover,…

We construct faces of the convex set of all $2\otimes 4$ bipartite separable states, which are affinely isomorphic to the simplex $\Delta_{9}$ with ten extreme points. Every interior point of these faces is a separable state which has a…

We show that the length of a qubit-qutrit separable state is equal to the max(r,s), where r is the rank of the state and s is the rank of its partial transpose. We refer to the ordered pair (r,s) as the birank of this state. We also…

We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS) states. First, we show that separability in the case of DS in $C^d\otimes C^d$ (symmetric qudits) can be…