Entanglement monotone derived from Grover’s algorithm
Ofer Biham, Michael A. Nielsen, Tobias J. Osborne · Physical Review A · 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 ${P}_{\mathrm{max}}$ that the search algorithm succeeds. We prove that, for pure states, ${P}_{\mathrm{max}}$ is an entanglement monotone, in the sense that ${P}_{\mathrm{max}}$ can never be decreased by local operations and classical communication.