Entanglement and the geometry of two qubits

Abstract

Two qubits is the simplest system where the notions of separable and entangled states and entanglement witnesses first appear. We give a three dimensional geometric description of these notions. This description however carries no quantitative information on the measure of entanglement. A four dimensional description captures also the entanglement measure. We give a neat formula for the Bell states which leads to a slick proof of the fundamental teleportation identity. We describe optimal distillation of two qubits geometrically and present a simple geometric proof of the Peres-Horodecki separability criterion.