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We analyse the use of entangled states to perform quantum computations nonlocally among distant nodes in a quantum network. The complexity associatedwith the generation of multiparticle entangled states is quantified in terms ofthe concept of global cost. This parameter allows us to compare the use ofphysical resources in different schemes. We show that for ideal channels andfor a sufficiently large number of nodes, the use of maximally entangled statesis advantageous over uncorrelated ones. For noisy channels, one has to useentanglement purification procedures in order to create entangled states ofhigh fidelity. We show that under certain circumstances a quantum networksupplied with a maximally entangled input still yields a smaller global cost,provided that $n$ belongs to a given interval $n\in [n_{min},n_{max}]$. Thevalues of $n_{min}$ and $n_{max}$ crucially depend on the purificationprotocols used to establish the $n$-- processor entangled states, as well as onthe presence of decoherence processes during the computation. The phaseestimation problem has been used to illustrate this fact.Comment: 8 pages (revtex), 3 figures; manuscript extended, figures adde

Distributed quantum computation over noisy channels