Geometry of entanglement witnesses parameterized by SO(3) group
Dariusz Chru\'sci\'nski, Filip A. Wudarski
TL;DR
This paper explores the geometric structure of entanglement witnesses in 4x4 matrices, parameterized by the SO(3) group, revealing two intersecting convex cones related to the topology of orthogonal groups.
Contribution
It characterizes a specific set of positive maps and entanglement witnesses parameterized by SO(3), analyzing their geometric and topological structure.
Findings
Identification of two intersecting convex cones in parameter space
Connection between the cones and the topology of SO(3)
Detailed geometric analysis of the entanglement witnesses
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.
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