Entanglement in the graph-state formalism

Abstract

We investigate the decoherence dynamics of a class of multi-particle entangled states - graph states - when subjected to individual noise processes. Recent analytical results for Pauli noise channels are summarized here. The power of this technique is demonstrated by making numerical calculations of entanglement for a relatively large system, which would be extremely tedious by brute force techniques alone. The results are numerically extended to linear graph states subjected to the generalized amplitude damping noise channel, which is an important case of a non-pauli noise channel. For small system sizes of linear graph states, the exact entanglement together with the lower and upper bounds are plotted. It is shown that in the limit of an in¯nite heat bath all these bounds coincide to give the exact entanglement decay.