Optimal discrimination between quantum operations

In this paper, we consider the problem of discriminating two given quantum operations. Based on the Bloch representation of a single qubit, we give an implicit expression that can be used to evaluate the exact minimum error probability of discriminating any two single-qubit quantum operations by unentangled input states. In particular, for the Pauli channels discussed in Sacchi (2005 Phys. Rev. A 71 062340), we use a more intuitive and visual method to deal with their discrimination problem. Also, we consider the condition for perfect discrimination of two quantum operations