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Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation

W. Dür·J. I. Cirac
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Abstract

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.

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W. Dür, J. I. Cirac. 2000-12-29. Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation. https://doi.org/10.1103/physreva.64.012317

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