The maximum rate at which classical information can be reliably transmitted
per use of a quantum channel strictly increases in general with N, the number
of channel outputs that are detected jointly by the quantum joint-detection
receiver (JDR). This phenomenon is known as superadditivity of the maximum
achievable information rate over a quantum channel. We study this phenomenon
for a pure-state classical-quantum (cq) channel and provide a lower bound on
CNβ/N, the maximum information rate when the JDR is restricted to making
joint measurements over no more than N quantum channel outputs, while
allowing arbitrary classical error correction. We also show the appearance of a
superadditivity phenomenon---of mathematical resemblance to the aforesaid
problem---in the channel capacity of a classical discrete memoryless channel
(DMC) when a concatenated coding scheme is employed, and the inner decoder is
forced to make hard decisions on N-length inner codewords. Using this
correspondence, we develop a unifying framework for the above two notions of
superadditivity, and show that for our lower bound to CNβ/N to be equal to a
given fraction of the asymptotic capacity C of the respective channel, N
must be proportional to V/C2, where V is the respective channel dispersion
quantity.Comment: To appear in IEEE Transactions on Information Theor