On entanglement in two-qubit system and torus action on Grassmannian Gr(2,4)


Laboratory of Information Technologies

Joint Laboratory Seminar

Date and Time: Wednesday, 13 February 2024, at 11:00 AM

Venue: room 310, Meshcheryakov Laboratory of Information Technologies, online on Webinar

Seminar topic: “On the entanglement in a two-qubit system and the torus action on the Grassmannian Gr(2,4)”

Speaker: Liudmila Bordag


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.