On Finite Blocklength Converse Bounds for Classical Communication Over Quantum Channels

We explore several new converse bounds for classical communication over quantum channels in the finite blocklength regime. First, we show that the Matthews-Wehner meta-converse bound for entanglement-assisted classical communication can be achieved by activated, no-signalling assisted codes, suitably generalizing a result for classical channels. Second, we derive a new meta-converse on the amount of information unassisted codes can transmit over a single use of a quantum channel. We further show that this meta-converse can be evaluated via semidefinite programming. As an application, we provide a second-order analysis of classical communication over quantum erasure channels.

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