Exchange-Free Computation on an Unknown Qubit at a Distance

Counterfactual communication has been demonstrated as a way of sending classical information without exchanging particles: exchange-free. Here we extend this to directly communicating an arbitrary qubit, not only exchange-free but crucially without the sender having to implement a quantum object locally, paving the way for feasible future demonstrations. More remarkably, we propose an exchange-free protocol that allows one party to directly enact, by means of a suitable program, any computation on a remote second party's unknown qubit. By then showing how to realise exchange-free control of a universal two-qubit gate, we enable the first party to directly enact in principle any desired algorithm on a remote second party's programmable quantum circuit.