  We introduce the task of random-receiver quantum communication, in which a
sender transmits a quantum message to a receiver chosen from a list of n
spatially separated parties. The choice of receiver is unknown to the sender,
but is known by the n parties, who coordinate their actions by exchanging
classical messages. In normal conditions, random-receiver quantum communication
requires a noiseless quantum communication channel from the sender to each of
the n receivers. In contrast, we show that random-receiver quantum
communication can take place through entanglement-breaking channels if the
order of such channels is controlled by a quantum bit that is accessible
through quantum measurements. Notably, this phenomenon cannot be mimicked by
allowing free quantum communication between the sender and any subset of k<n
parties.
