  We discuss the fidelity as a figure of merit in quantum error correction
schemes. We show that when identifiable but uncorrectable errors occur as a
result of the action of the channel, a common strategy that improves the
fidelity actually decreases the transmitted mutual information. The conclusion
is that while the fidelity is simple to calculate and therefore often used, it
is perhaps not always a recommendable figure of merit for quantum error
correction. The reason is that while it roughly speaking encourages
optimisation of the "mean probability of success", it gives no incentive for a
protocol to indicate exactly where the errors lurk. For small error
probabilities, the latter information is more important for the integrity of
the information than optimising the mean probability of success.
