Geometry in the Entanglement Dynamics of the Double Jaynes-Cummings Model

We report on the geometric character of the entanglement dynamics of two pairs of qubits evolving according to the double Jaynes-Cummings model. We show that the entanglement dynamics for the initial states (sic)psi(0)> = cos alpha (sic) 0 > + sin alpha (sic) 1 > and (sic)(0)> = cos alpha (sic) 1 > + sin alpha (sic) 0 > cover three-dimensional surfaces in the diagram C-ij x C-ik x C-il, where C-mn stands for the concurrence between qubits m and n, varying 0 <= alpha <= pi)2. In the first case, projections of the surfaces on a diagram C-ij x C-kl are conics. In the second case, curves can be more complex. We relate those conics with a measurable quantity, the predictability. We also derive inequalities limiting the sum of the squares of the concurrence of every bipartition and show that sudden death of entanglement is intimately connected to the size of the average radius of a hypersphere.