Division of the two-qubit Hilbert space according to the entanglement sudden death under composite noise environment

Abstract

We show theoretically that according to the disentanglement behavior under composite noise environment, the Hilbert space of a two-qubit system can be divided into two separate parts: a 3-dimensional subspace in which all states disentangle asymptotically, and the rest in which all states disentangle abruptly. The violation of additivity for entanglement decay rates under weak noises [see, PRL 97, 140403 (2006)] therefore can be explained in terms of such division of the Hilbert space.