Geometry of entanglement witnesses parameterized by SO(3) group

Abstract

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.

10 pages

References in corpus (2)

• Entanglement detection
• Structural approximations to positive maps and entanglement breaking channels

Cited by in corpus (2)

• A class of symmetric Bell diagonal entanglement witnesses - a geometric perspective
• On Kossakowski construction of positive maps in matrix algebras