Communication Power of a Noisy Qubit

A fundamental limitation of quantum communication is that a single qubit can carry at most one bit of classical information. For an important class of quantum communication channels, known as entanglement breaking, this limitation holds even if the sender and receiver share entangled particles. But does this mean that, for the purpose of communicating classical messages, a noisy entanglement-breaking qubit channel can be replaced by a noisy bit channel? Here we answer the question in the negative. We introduce a game, similar to the Monty Hall problem in classical statistics, where a sender assists a receiver in finding a valuable item (the "prize") hidden in one of four possible boxes, while avoiding a hazardous item (the "bomb") hidden in one of the remaining three boxes. We show that no classical strategy using a noisy bit channel can ensure that the bomb is avoided, even if the sender and receiver share arbitrary amounts of randomness. In contrast, communication of a qubit through a class of noisy entanglement-breaking channels, which we call quantum not channels, allows the players to deterministically avoid the bomb and to find the prize with a guaranteed nonzero probability. Our findings show that the communication of classical messages through a noisy entanglement-breaking qubit channel assisted by quantum entanglement cannot, in general, be simulated by communication through a noisy bit channel assisted by classical correlations.