Abstract:

The entanglement characteristics of 2-qubits states are encoded in the orbit space of the subgroup SU(2) x SU(2) of the unitary SU(4) group acting on the qubit’s state space. Correspondingly, from geometrical point of view, the problem to describe the entanglement of two qubits in the general case can be reduced to a study the action of the real three dimensional torus on the Grassmannian Gr(2,4). Using the Plücker coordinates, we describe all invariant structures of this fiber bundle with an appropriate parametrization of them. A projective mapping of the image of this fiber bundle from five-dimensional projective space into three-dimensional real space is given.