Entanglement can increase asymptotic rates of zero-error classical communication over classical channels

It is known that the number of different classical messages which can be communicated with a single use of a classical channel with zero probability of decoding error can sometimes be increased by using entanglement shared between sender and receiver. It has been an open question to determine whether entanglement can ever offer an advantage in terms of the zero-error communication rates achievable in the limit of many channel uses. In this paper we show, by explicit examples, that entanglement can indeed increase asymptotic zero-error capacity. Interestingly, in our examples the quantum protocols are based on the root systems of the exceptional Lie groups E7 and E8.