The limits of enhancing communication rates with entanglement

Entanglement has long been recognized as a powerful resource for improving communication rates between a sender and receiver over a noisy quantum channel. But to what extent can entanglement enhance the communication rates that are achievable for a given quantum channel?

In one of the earliest works on entanglement-assisted communication, it is conjectured that the ratio of rates which are achievable with and without entanglement-assistance is bounded by a function that depends only on the channel's output dimension. Here, we show that this conjecture holds for a large class of quantum channels. We further show that a corresponding conjecture does not hold for communication under adversarial quantum noise.