  Known strategies for sending bits at the capacity rate over a general channel
with classical input and quantum output (a cq channel) require the decoder to
implement impractically complicated collective measurements. Here, we show that
a fully collective strategy is not necessary in order to recover all of the
information bits. In fact, when coding for a large number N uses of a cq
channel W, N I(W_acc) of the bits can be recovered by a non-collective strategy
which amounts to coherent quantum processing of the results of product
measurements, where I(W_acc) is the accessible information of the channel W. In
order to decode the other N (I(W) - I(W_acc)) bits, where I(W) is the Holevo
rate, our conclusion is that the receiver should employ collective
measurements. We also present two other results: 1) collective Fuchs-Caves
measurements (quantum likelihood ratio measurements) can be used at the
receiver to achieve the Holevo rate and 2) we give an explicit form of the
Helstrom measurements used in small-size polar codes. The main approach used to
demonstrate these results is a quantum extension of Arikan's polar codes.
