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Phys. Rev. A 65, 062312 (2002) [7 pages]

Entanglement monotone derived from Grover’s algorithm

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Ofer Biham1,2, Michael A. Nielsen1,3, and Tobias J. Osborne1,3
1Centre for Quantum Computer Technology and Department of Physics, University of Queensland, Brisbane, Queensland 4072, Australia
2Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
3Institute for Theoretical Physics, Kohn Hall, University of California Santa Barbara, Santa Barbara, California 93106

Received 17 December 2001; published 13 June 2002

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 the 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 Pmax that the search algorithm succeeds. We prove that, for pure states, Pmax is an entanglement monotone, in the sense that Pmax can never be decreased by local operations and classical communication.

© 2002 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.65.062312
DOI:
10.1103/PhysRevA.65.062312
PACS:
03.67.Lx, 89.70.+c
 
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