Strong Converse Exponent for Entanglement-Assisted Communication
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Entanglement-assisted classical capacity is regarded as the natural quantum generalization of the classical capacity of a classical channel. We determine the exact strong converse exponent for entanglement-assisted classical communication. Our main contribution is the derivation of an upper bound for the strong converse exponent which is characterized by the sandwiched Rényi divergence. It turns out that this upper bound coincides with the lower bound of Gupta and Wilde (Commun Math Phys 334:867–887, 2015). Thus, the strong converse exponent follows from the combination of these two bounds. Our result also implies that the exponential bound for the strong converse property of quantum-feedback-assisted classical communication, derived by Cooney, Mosonyi and Wilde (Commun Math Phys 344:797–829, 2016), is optimal. Hence, we have determined the exact strong converse exponent for this problem as well. This shows that additional feedback does not affect the strong converse exponent of entanglement-assisted classical communication. The above findings can be extended to deal with the transmission of quantum information in the same settings, yielding similar results.
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