  A source assumed to prepare a specified reference state sometimes prepares an
anomalous one. We address the task of identifying these anomalous states in a
series of $n$ preparations with $k$ anomalies. We analyse the minimum-error
protocol and the zero-error (unambiguous) protocol and obtain closed
expressions for the success probability when both reference and anomalous
states are known to the observer and anomalies can appear equally likely in any
position of the preparation series. We find the solution using results from
association schemes theory. In particular we use the Johnson association scheme
which arises naturally from the Gram matrix of this problem. We also study the
regime of large $n$ and obtain the expression of the success probability that
is non-vanishing. Finally, we address the case in which the observer is blind
to the reference and the anomalous states. This scenario requires an universal
protocol for which we prove that in the asymptotic limit the success
probability correspond to average of the known state scenario.

Quantum Physics