43 research outputs found
Constructing new optimal entanglement witnesses
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 entanglement encoded into states with positive partial transposition
(PPT). Equivalently, we provide a new construction of indecomposable atomic
maps in the algebra of 2k x 2k complex matrices. It is shown that their
structural physical approximations give rise to entanglement breaking channels.
This result supports recent conjecture by Korbicz et. al.Comment: 9 page
Geometry of entanglement witnesses for two qutrits
We characterize a convex subset of entanglement witnesses for two qutrits.
Equivalently, we provide a characterization of the set of positive maps in the
matrix algebra of 3 x 3 complex matrices. It turns out that boundary of this
set displays elegant representation in terms of SO(2) rotations. We conjecture
that maps parameterized by rotations are optimal, i.e. they provide the
strongest tool for detecting quantum entanglement. As a byproduct we found a
new class of decomposable entanglement witnesses parameterized by improper
rotations from the orthogonal group O(2).Comment: 9 page
Constructing optimal entanglement witnesses. II
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 provides natural generalization of the Robertson map. It is shown
that their structural physical approximations give rise to entanglement
breaking channels.Comment: 6 page
A class of positive atomic maps
We construct a new class of positive indecomposable maps in the algebra of `d x d' complex matrices. These maps are characterized by the `weakest' positivity property and for this reason they are called atomic. This class provides a new reach family of atomic entanglement witnesses which define important tool for investigating quantum entanglement. It turns out that they are able to detect states with the `weakest' quantum entanglement
Geometry of entanglement witnesses parameterized by SO(3) group
We characterize a set of positive maps in matrix algebra of 4x4 complex
matrices. Equivalently, we provide a subset of entanglement witnesses
parameterized by the rotation group SO(3). Interestingly, these maps/witnesses
define two intersecting convex cones in the 3-dimensional parameter space. The
existence of two cones is related to the topological structure of the
underlying orthogonal group. We perform detailed analysis of the corresponding
geometric structure.Comment: 10 page
Entanglement witnesses arising from Choi type positive linear maps
We construct optimal PPTES witnesses to detect PPT entangled
edge states of type constructed recently \cite{kye_osaka}. To do this,
we consider positive linear maps which are variants of the Choi type map
involving complex numbers, and examine several notions related to optimality
for those entanglement witnesses. Through the discussion, we suggest a method
to check the optimality of entanglement witnesses without the spanning
property.Comment: 18 pages, 4 figures, 1 tabl