W. Dur et Ji. Cirac, Nonlocal operations: Purification, storage, compression, tomography, and probabilistic implementation - art. no. 012317, PHYS REV A, 6401(1), 2001, pp. 2317
We provide several applications of a previously introduced isomorphism betw
een physical operations acting on two systems and entangled states [Phys. R
ev. Lett. 86, 544 (2001)]. We show (i) how to implement (weakly) nonlocal t
wo-qubit unitary operations with a small amount of entanglement; (ii) that
a known, noisy, nonlocal unitary operation as well as an unknown, noisy, lo
cal unitary operation can be purified; (iii) how to perform the tomography
of arbitrary, unknown, nonlocal operations; (iv) that a set of local unitar
y operations as well as a set of nonlocal unitary operations can be stored
and compressed; and (v) how to implement probabilistically two-qubit gates
for photons. We also show how to compress a set of bipartite entangled stat
es locally, as well as how to implement certain nonlocal measurements using
a small amount of entanglement. Finally, we generalize some of our results
to multiparty systems.