Related papers: Constructing new optimal entanglement witnesses

An entanglement witness (EW) is an operator that allows to detect entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e. to detect entangled states in an optimal way. We show how to optimize…

We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…

We provide a canonical form of mixed states in bipartite quantum systems in terms of a convex combination of a separable state and a, so-called, edge state. We construct entanglement witnesses for all edge states. We present a canonical…

We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map Phi which operates on state spaces with even dimension N >= 4. It is shown that Phi detects many entangled states…

We construct optimal PPTES witnesses to detect $3\otimes 3$ PPT entangled edge states of type $(6,8)$ constructed recently \cite{kye_osaka}. To do this, we consider positive linear maps which are variants of the Choi type map involving…

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;…

A new class of entanglement witnesses (EWs) called reduction type entanglement witnesses is introduced, which can detect some multi-qudit entangeled states including PPT ones with Hilbert space of dimension $d_{_{1}}\otimes…

We show that the entanglement witnesses based on local orthogonal observables which are introduced in [S. Yu and N.-L. Liu, Phys. Rev. Lett. 95, 150504 (2005)] and [O. G\"uhne, M. Mechler, G. T\'oth and P. Adam, Phys. Rev. A 74, 010301…

We introduce a new entanglement measure based on optimal entanglement witness. First of all, we show that the entanglement measure satisfies some necessary properties, including zero entanglements for all separable states, convexity,…

We construct both nonlinear and linear entanglement witnesses, by tensoring and partial tracing existing states and witnesses. We show that little shared quantum resources allow to employ decomposable witnesses to obtain larger ones…

We study the optimal entanglement witness with respect to multiqubits W-states. We show such entanglement witnesses can be used to distinguish genuine entangled states, different biseparable states and fully separable states.

A new family of positive, trace-preserving maps is introduced. It is defined using the mutually unbiased measurements, which generalize the notion of mutual unbiasedness of orthonormal bases. This family allows one to define entanglement…

We define an entanglement witness in a composite quantum system as an observable having nonnegative expectation value in every separable state. Then a state is entangled if and only if it has a negative expectation value of some…

We provide a class of positive and trace-preserving maps based on symmetric measurements. From these positive maps we present separability criteria, entanglement witnesses, as well as the lower bounds of concurrence. We show by detailed…

One of the interesting problems on optimal indecomposable entanglement witnesses is whether there exists an optimal indecomposable witness which neither has the spanning property nor is associated with extremal positive linear map. Here, we…

Two approaches can be utilized to handle the separability problem, finding out whether a given bipartite qudit state is separable or not: a direct procedure on the state space or the effective tool of entanglement witnesses (EWs). This…

Entanglement witnesses are invaluable for efficient quantum entanglement certification without the need for expensive quantum state tomography. Yet, standard entanglement witnessing requires multiple measurements and its bounds can be…

We consider bipartite quantum state discrimination using positive-partial-transpose measurements and show that minimum-error discrimination by positive-partial-transpose measurements is closely related to entanglement witness. By using the…

It is well known that so called Breuer-Hall positive maps used in entanglement theory are optimal. We show that these maps possess much more subtle property --- they are exposed. As a byproduct it proves that a Robertson map in the algebra…

Quantum entanglement lies at the heart of quantum mechanics and quantum information processing. In this work, we show a new framework where entangled states play the role of witnesses. We extend the notion of entanglement witnesses,…