Abstract: We consider the problem of distinguishing two quantum operations with parallel scheme. A necessary condition for the success of discrimination is formulated, which only connects to the set generated by the Kraus operators. We establish the relation of this method with numerical range, and use some techniques there to solve some cases of the problem. When the set generated by the Kraus operators has only two elements, some interesting examples will be examined, and some conjectures will be raised.

Date: 23 September 2015