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arXiv · 1405.1797

On the Second-Order Asymptotics for Entanglement-Assisted Communication

Nilanjana Datta·Marco Tomamichel·Mark M. Wilde
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Abstract

The entanglement-assisted classical capacity of a quantum channel is known to provide the formal quantum generalization of Shannon's classical channel capacity theorem, in the sense that it admits a single-letter characterization in terms of the quantum mutual information and does not increase in the presence of a noiseless quantum feedback channel from receiver to sender. In this work, we investigate second-order asymptotics of the entanglement-assisted classical communication task. That is, we consider how quickly the rates of entanglement-assisted codes converge to the entanglement-assisted classical capacity of a channel as a function of the number of channel uses and the error tolerance. We define a quantum generalization of the mutual information variance of a channel in the entanglement-assisted setting. For covariant channels, we show that this quantity is equal to the channel dispersion, and thus completely characterize the convergence towards the entanglement-assisted classical capacity when the number of channel uses increases. Our results also apply to entanglement-assisted quantum communication, due to the equivalence between entanglement-assisted classical and quantum communication established by the teleportation and super-dense coding protocols.

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Nilanjana Datta, Marco Tomamichel, Mark M. Wilde. 2016-02-08. On the Second-Order Asymptotics for Entanglement-Assisted Communication. https://doi.org/10.1007/s11128-016-1272-5

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