Controlled Bidirectional Remote Implementation of Arbitrary Unknown Single-Qubit Operations via a High-Dimensional Quantum Channel
Consider two remote laboratories: Alice holds an unknown input |ξ⟩ and a private single-qubit unitary UA, while Bob holds |η⟩ and UB. We present an exact local-operations-and-classical-communication protocol that produces UB|ξ⟩ at Alice’s site and UA|η⟩ at Bob’s site only after the controller labels are released. A fiv...