  We provide several applications of a previously introduced isomorphism
between physical operations acting on two systems and entangled states [1]. We
show: (i) how to implement (weakly) non-local two qubit unitary operations with
a small amount of entanglement; (ii) that a known, noisy, non-local unitary
operation as well as an unknown, noisy, local unitary operation can be
purified; (iii) how to perform the tomography of arbitrary, unknown, non-local
operations; (iv) that a set of local unitary operations as well as a set of
non-local unitary operations can be stored and compressed; (v) how to implement
probabilistically two-qubit gates for photons. We also show how to compress a
set of bipartite entangled states locally, as well as how to implement certain
non-local measurements using a small amount of entanglement. Finally, we
generalize some of our results to multiparty systems.
