On the second-order asymptotics for entanglement-assisted communication |
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Authors: | Nilanjana Datta Marco Tomamichel " target="_blank">Mark M Wilde |
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Affiliation: | 1.Statistical Laboratory, Centre for Mathematical Sciences,University of Cambridge,Cambridge,UK;2.Centre for Quantum Technologies,National University of Singapore,Singapore,Singapore;3.School of Physics,The University of Sydney,Sydney,Australia;4.Department of Physics and Astronomy, Center for Computation and Technology, Hearne Institute for Theoretical Physics,Louisiana State University,Baton Rouge,USA |
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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 toward 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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