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We provide several applications of a previously introduced isomorphismbetween physical operations acting on two systems and entangled states [1]. Weshow: (i) how to implement (weakly) non-local two qubit unitary operations witha small amount of entanglement; (ii) that a known, noisy, non-local unitaryoperation as well as an unknown, noisy, local unitary operation can bepurified; (iii) how to perform the tomography of arbitrary, unknown, non-localoperations; (iv) that a set of local unitary operations as well as a set ofnon-local unitary operations can be stored and compressed; (v) how to implementprobabilistically two-qubit gates for photons. We also show how to compress aset of bipartite entangled states locally, as well as how to implement certainnon-local measurements using a small amount of entanglement. Finally, wegeneralize some of our results to multiparty systems.Comment: 15 pages, no figure

Nonlocal operations: Purification, storage, compression, tomography, and probabilistic implementation