system onto one of a complete set of mutually orthogonal states. In this case the set of states is chosen to be the basis in which the coding states are diagonal.) With this choice of coding states and measurement the channel is classical, in that it can be implemented with a classical system. The Holevo bound takes into account that the sender may only be able to send mixed states, and this mixing reduces the amount of information that can be transmitted. However, if the receiver is not able to perform measurements which always project the system to a pure state (so called [*complete*]{} measurements), then in general the information will be further reduced. In 1996 Schumacher, Westmoreland and Wootters showed that when the receivers measurement is incomplete, it is possible to take this into account and derive a more stringent bound on the information. If the receiver’s measurement is the POVM described by the operators $\{A_j\}$ (with $\sum_j
A_j^\dagger A_j = 1$), so that the measurement outcomes are labeled by the index $j$, then the SWW bound is [@SWW] $$M(I\! :\! J) \leq \chi - \sum_j P(j) \chi_j ,
  \label{SWW}$$ where $P(j)$ is the probability of outcome $j$ [@note1], 