Distributed quantum computation over noisy channels

We analyse the use of entangled states to perform quantum computations non locally among distant nodes in a quantum network. The complexity associated with the generation of multiparticle entangled states is quantified in terms of the concept of global cost. This parameter allows us to compare the use of physical resources in different schemes. We show that for ideal channels and for a sufficiently large number of nodes, the use of maximally entangled states is advantageous over uncorrelated ones. For noisy channels, one has to use entanglement purification procedures in order to create entangled states of high fidelity.