Julio I. de Vicente, Cornelia Spee, Barbara Kraus
Entanglement is a resource in quantum information theory when state manipulation is restricted to Local Operations assisted by Classical Communication (LOCC). It is, therefore, of paramount importance to decide which LOCC transformations are possible and, particularly, which states are maximally useful under this restriction. While the bipartite maximally entangled state is well known (it is the only state that cannot be obtained from any other and, at the same time, it can be transformed to any other by LOCC), no such state exists in the multipartite case. In order to scope with this fact, we introduce here the notion of the Maximally Entangled Set (MES) of n-partite states. This is the set of states which are maximally useful under LOCC manipulation, i. e. any state outside of this set can be obtained via LOCC from one of the states within the set and no state in the set can be obtained from any other state via LOCC. We determine the MES for three and four qubit states and provide a simple characterization for them. In both cases, infinitely many states are required. However, while the MES is of zero-measure for 3-qubit states, almost all 4-qubit states are in the MES. This is because, in contrast to the 3-qubit case, deterministic LOCC transformations are almost never possible among fully entangled four-partite states. We determine the zero-measure subset of the MES of LOCC convertible states. This is the only relevant class of states for entanglement manipulation.
View original:
http://arxiv.org/abs/1305.7398
No comments:
Post a Comment