aradox is quite simple. In Chapter 21, we have considered the action of encoding and decoding classical information into or from a suite of quantum symbols Px from an alphabet {pi}, to be conveyed through some ideal quantum channel. The operation of encoding is the "preparation" of the state Px, which means that the originator sets up the quantum system in the state Px. The operation of decoding is the "measurement" by the recipient of any received symbol Py, using the adequate POVM set for the identification of each symbol possibility. The full encoding and decoding operation can be virtually reduced into a classical information channel that relates two random sources X and Y. As we have learnt, the mutual information H(X; Y) is bounded by H(X), just as in the purely classical case, but the quantum channel introduces the extra (Holevo) bound X such that H(X;Y)<X<H(X). (23.43) As we have also seen, if the symbols Pi have orthogonal support in {pi}, meaning that different qubit symbols are necessarily orthogonal, then X = H(X) and the Holevo bound is reduced to the originator source entropy, which obliterates any particularity of using a quantum channel as opposed to a purely classical one. Consider next the case of the noisy quantum channel. The encoding and decoding oper- ations are conceptually the same as previously, except that decoding (POVM measure- ment) is performed onto message codewords, defined by Om2 8 Quantum channel noise and channel capacity given the originator codeword PM = Pm X Pm2 x Pmn. In the received message OM, each symbol Omk is the result of a quantum operation E such that Omk = E(Pmk). From statistical measurements, the recipient may then compute X' = S((o)) - (S(o)) = S[(&(p))] - (S[E(p)]) for the source o, but it is irrelevant to call this quantity a "Holevo bound," because of the quantum operation E introduced by the channel, which, for each recipient symbol Omk, has corrupted the reference symbol Pmk If E is not a "noiseless" constant, therefore, the action of decoding is conceptuall