title: Entanglement cost of implementing controlled-unitary operations.
abstract: We investigate the minimum entanglement cost of the deterministic implementation of two-qubit controlled-unitary operations using local operations and classical communication (LOCC). We show that any such operation can be implemented by a three-turn LOCC protocol, which requires at least 1 ebit of entanglement when the resource is given by a bipartite entangled state with Schmidt number 2. Our result implies that there is a gap between the minimum entanglement cost and the entangling power of controlled-unitary operations. This gap arises due to the requirement of implementing the operations while oblivious to the identity of the inputs.
authors: Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan.
authors: Akihito
authors: A
authors: Soeda
authors: Peter S
authors: PS
authors: Turner
authors: Mio
authors: M
authors: Murao