Strong Converse Exponent for Entanglement-Assisted Communication

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 R{\'e}nyi 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.