Entanglement sudden-death time: a geometric quantity

We study the entanglement evolution of the set of Bell diagonal states for a two-qubit system coupled to two independent vacuum noise sources. This set can be represented geometrically as the set of points inside a tetrahedron in a three-dimensional Euclidean space and contains the maximally entangled states for bipartite systems. We show that the set of entangled Bell diagonal states can be divided into two bounded subsets in this representation: states that evolve into separable states in a finite time and states that lose their entanglement asymptotically. Additionally, we find that the finite time in which the Bell diagonal states lose their entanglement depends only on the distances from their position in the three-dimensional representation to the boundaries of both, the set of separable states and the set of states that remains always entangled.