About distillability of depolarized states

Quantum information is mostly based on use of entanglement, and optimal performances of quantum protocols are obtained when the parties share maximally entangled states. However, entanglement is corrupted by the interaction with the environment, and it becomes crucial to establish whether or not quantum protocols may be exploited for a given level of the environmental noise. Quantum purification consists [1] in distilling a certain number of maximally entangled states from a larger number of corrupted states, i.e. to sacrifice some copies of the received state to increase the entanglement of others. Entanglement of partially corrupted states is only a necessary conditions for distillation, bound entanglement being the entanglement that cannot be distilled [2]. Some sufficient criterion for distillability has been proposed, the most relevant being the Reduction Criterion (RC) [3], and the norm-related criterions [4]. In this paper we apply the RC to a generalized class of depolarized states in d dimensions. First we briefly review the distillability criterion and introduce a characteristic polynomial for our class of states. Then we apply our results to 3× 3 bypartite systems and numerically study the distillability.