Unambiguous comparison of unitary channels

We address the problem of an unambiguous comparison of a pair of unknown qudit unitary channels. Using the framework of process positive operator valued measures we characterize all solutions and identify the optimal ones. We prove that the entanglement is the key ingredient in designing the optimal experiment for comparison of unitary channels. Without entanglement the optimality cannot be achieved. The proposed scheme is also experimentally feasible.

Figure 1

Experiment for comparison of two unitary channels ${\mathcal{E}}_U,{\mathcal{E}}_V$.