Random-Receiver Quantum Communication

Abstract

We introduce the task of random-receiver quantum communication, in which a sender transmits a quantum message to a receiver selected from a list of n spatially separated parties. At the moment of transmission, the choice of receiver is unknown to the sender. Later, it becomes known to the n parties, who coordinate their actions by exchanging classical messages. In normal conditions, random-receiver quantum communication requires a noiseless quantum communication channel between the sender and each of the n receivers. In contrast, we show that random-receiver quantum communication can take place through noisy, entanglement-breaking channels if the order of such channels is coherently controlled by a quantum bit that is accessible through measurements. While this phenomenon is achieved with a single control qubit, it cannot be mimicked by adding a noiseless qubit channel from the sender to any of the receivers, or more generally, from the sender to any subset of k<n parties.