Entanglement monotone derived from Grover's algorithm

Ofer Biham, Michael A. Nielsen, Tobias J. Osborne
2002 Physical Review A. Atomic, Molecular, and Optical Physics  
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,
more » ... n the sense that P_max can never be decreased by local operations and classical communication.
doi:10.1103/physreva.65.062312 fatcat:bejkdouoo5c3vmphfrjdsdg27m