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

Abstract

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 increase 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, even to the extent that it is equal to the normal capacity of the channel. Interestingly, our examples are based on the exceptional simple root systems E7 and E8.

14 pages, 2 figure

References in corpus (5)

• Improving zero-error classical communication with entanglement
• Entanglement-Enhanced Classical Communication over a Noisy Classical Channel
• Factor-Group-Generated Polar Spaces and (Multi-)Qudits
• Entanglement-assisted zero-error capacity is upper bounded by the Lovasz theta function
• Exceptional and Non-crystallographic Root Systems and the Kochen-Specker Theorem

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