Discrimination of POVMs with rank-one effects

The main goal of this work is to provide an insight into the problem of discrimination of positive operator-valued measures with rank-one effects. It is our intention to study multiple-shot discrimination of such measurements, that is the case when we are able to use to unknown measurement a given number of times. Furthermore, we are interested in comparing two possible discrimination schemes: the parallel and adaptive ones. To this end, we construct a pair of symmetric informationally complete positive operator-valued measures which can be perfectly discriminated in a two-shot adaptive scheme but cannot be distinguished in the parallel scheme. On top of this, we provide an explicit algorithm which allows us to find this adaptive scheme.