Physics – Quantum Physics
Scientific paper
2005-03-24
Physics
Quantum Physics
16 pages, no figures
Scientific paper
Let B_1,B_2 be balls in finite-dimensional real vector spaces E_1,E_2, centered around unit length vectors v_1,v_2 and not containing zero. An element in the tensor product space E_1 \otimes E_2 is called B_1 \otimes B_2-separable if it is contained in the convex conic hull of elements of the form w_1 \otimes w_2, where w_1 \in B_1, w_2 \in B_2. We study the cone formed by the separable elements in E_1 \otimes E_2. We determine the largest faces of this cone via a description of the extreme rays of the dual cone, i.e. the cone of the corresponding positive linear maps. We compute the radius of the largest ball centered around v_1 \otimes v_2 that consists of separable elements. As an application we obtain lower bounds on the radius of the largest ball of separable unnormalized states around the identity matrix for a multi-qubit system. These bounds are approximately 12% better than the best previously known. Our results are extendible to the case where B_1,B_2 are solid ellipsoids.
No associations
LandOfFree
Cones of ball-ball separable elements does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Cones of ball-ball separable elements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cones of ball-ball separable elements will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-587079