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An entanglement monotone derived from Grover's algorithm

Ofer Biham·Michael A. Nielsen·Tobias J. Osborne
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Abstract

This paper demonstrates that how well a state performs as an input to Grover's search algorithm depends critically upon the entanglement present in that state; the more entanglement, the less well the algorithm performs. More precisely, suppose we take a pure state input, and prior to running the algorithm apply local unitary operations to each qubit in order to maximize the probability P_max that the search algorithm succeeds. We prove that, for pure states, P_max is an entanglement monotone, in the sense that P_max can never be decreased by local operations and classical communication.

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Ofer Biham, Michael A. Nielsen, Tobias J. Osborne. 2001-12-17. An entanglement monotone derived from Grover's algorithm. https://doi.org/10.1103/physreva.65.062312

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