Essentially optimal gate teleportation

Abstract

Gate teleportation allows us to implement a nonlocal unitary using local operations, classical communication (LOCC), and a shared entangled state. Known deterministic teleportation protocols consume at least one full ebit and achieve optimal entanglement consumption only for Clifford gates. Here, we present a deterministic LOCC protocol for implementing the two-qubit controlled-phase gate $U_{\phi}=\mathrm{diag}(1,1,1,e^{i \phi})$ with $\phi \in [0,\pi]$ whose entanglement consumption is close to optimal for every $\phi$. In particular, vanishing rotation angles require vanishing entanglement.