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Purifying Noisy Entanglement Requires Collective Measurements

Linden, N.; Massar, S.; Popescu, Sandu


Keyword(s): quantum mechanics; quantum information; quantum non- locality; entanglement

Abstract: Known entanglement purification protocols for mixed states use collective measurements on several copies of the state in order to increase the entanglement of some of them. We address the question of whether it is possible to purify the entanglement of a state by processing each copy separately. While this is possible for pure states, we show that this is impossible, in general, for mixed states. The importance of this result both conceptually and for experimental realization of purification is discussed. We also give explicit invariants of an entangled state of two qubits under local actions and classical communication. Notes: N. Linden, Isaac Newton Institute for Mathematical Sciences, Cambridge, CB3 0EH, UK S.Massar, Institute for Theoretical Physics, Princetonplein 5, PO Box 80006, 3508 TA Utrecht, The Netherlands

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