Entanglement cost of implementing controlled-unitary operations

Phys Rev Lett. 2011 Oct 28;107(18):180501. doi: 10.1103/PhysRevLett.107.180501. Epub 2011 Oct 25.

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.