A method to compute the optimal success probability of discrimination of $N$ arbitrary quantum states is presented, based on the decomposition of any $N$-outcome measurement into sequences of nested two-outcome ones. In this way the optimization of the measurement operators can be carried out in successive steps, optimizing first the binary measurements at the deepest nesting level and then moving on to those at higher levels. We obtain an analytical expression for the maximum success probability after the first optimization step and examine its form for the specific case of $N=3,4$ states of a qubit. In this case, at variance with previous proposals, we are able to provide a compact expression for the success probability of any set of states, whose numerical optimization is straightforward; the results thus obtained highlight some lesser-known features of the discrimination problem.

• Received 9 January 2017

DOI:https://doi.org/10.1103/PhysRevA.95.042307