TY - JOUR
T1 - Optimal state discrimination and unstructured search in nonlinear quantum mechanics
JF - Physical Review A
Y1 - 2016
A1 - Andrew M. Childs
A1 - Joshua Young
AB - 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.
VL - 93
U4 - 022314
UR - http://arxiv.org/abs/1507.06334
CP - 2
U5 - 10.1103/PhysRevA.93.022314
ER -