The communication power of a noisy qubit

TL;DR

This paper demonstrates that noisy entanglement-breaking qubit channels, specifically quantum NOT channels, can outperform classical bit channels in certain communication tasks, revealing a fundamental quantum advantage in classical information transmission.

Contribution

The authors introduce a game illustrating that quantum channels can deterministically outperform classical channels in avoiding hazards, showing a fundamental difference in classical communication capabilities.

Findings

Quantum NOT channels enable guaranteed hazard avoidance in the game.

Classical noisy bit channels cannot ensure hazard avoidance, even with shared randomness.

Quantum channels cannot be simulated by classical channels in this context.

Abstract

A fundamental limitation of quantum communication is that a single qubit can carry at most 1 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 into 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.