01395nas a2200145 4500008004100000245008900041210006900130260001500199300001100214490000700225520094000232100002301172700001801195856003601213 2016 eng d00aOptimal state discrimination and unstructured search in nonlinear quantum mechanics0 aOptimal state discrimination and unstructured search in nonlinea c2016/02/11 a0223140 v933 a Nonlinear variants of quantum mechanics can solve tasks that are impossible
in standard quantum theory, such as perfectly distinguishing nonorthogonal
states. Here we derive the optimal protocol for distinguishing two states of a
qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum
mechanics that arises as an effective description of Bose-Einstein condensates.
Using this protocol, we present an algorithm for unstructured search in the
Gross-Pitaevskii model, obtaining an exponential improvement over a previous
algorithm of Meyer and Wong. This result establishes a limitation on the
effectiveness of the Gross-Pitaevskii approximation. More generally, we
demonstrate similar behavior under a family of related nonlinearities, giving
evidence that the ability to quickly discriminate nonorthogonal states and
thereby solve unstructured search is a generic feature of nonlinear quantum
mechanics.
1 aChilds, Andrew, M.1 aYoung, Joshua uhttp://arxiv.org/abs/1507.06334