Geometry of Entanglement Witnesses Parametrized by SO(3) Group

We characterize a set of positive maps in matrix algebra of 4 × 4 complex matrices. Equivalently, we provide a subset of entanglement witnesses in ℂ4⊗ℂ4 parametrized 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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