Optimal universal and state-dependent quantum cloning

TLDR

The study establishes optimal quantum cloning machines that produce two clones from a single input, including both universal and state‑dependent cloners for any two nonorthogonal states, and discusses their fidelities and required auxiliary resources. The authors analyze universal and state‑dependent cloners, showing that optimal universal cloning can be realized via a special unitary evolution or a teleportation scheme, and construct optimal state‑dependent cloners for arbitrary nonorthogonal states. Universal cloners achieve a maximal fidelity of 5/6, and this result provides an upper bound on the quantum capacity of the depolarizing channel.

Abstract

We establish the best possible approximation to a perfect quantum cloning machine that produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two nonorthogonal states and discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive an upper bound on the quantum capacity of the depolarizing quantum channel.