Unambiguous identification of coherent states: Searching a quantum database

Abstract

We consider an unambiguous identification of an unknown coherent state with one of two unknown coherent reference states. Specifically, we consider two modes of an electromagnetic field prepared in unknown coherent states $\ensuremath{\mid}{\ensuremath{\alpha}}_{1}⟩$ and $\ensuremath{\mid}{\ensuremath{\alpha}}_{2}⟩$, respectively. The third mode is prepared either in the state $\ensuremath{\mid}{\ensuremath{\alpha}}_{1}⟩$ or in the state $\ensuremath{\mid}{\ensuremath{\alpha}}_{2}⟩$. The task is to identify (unambiguously) which of the two modes are in the same state. We present a scheme consisting of three beam splitters capable to perform this task. Although we do not prove the optimality, we show that the performance of the proposed setup is better than the generalization of the optimal measurement known for a finite-dimensional case. We show that a single beam splitter is capable to perform an unambiguous quantum state comparison for coherent states optimally. Finally, we propose an experimental setup consisting of $2N\ensuremath{-}1$ beam splitters for unambiguous identification among $N$ unknown coherent states. This setup can be considered as a search in a quantum database. The elements of the database are unknown coherent states encoded in different modes of an electromagnetic field. The task is to specify the two modes that are excited in the same, though unknown, coherent state.