**Optimal quantum learning of an unknown unitary transformation and multiround reference frame alignment** - Giulio Chiribella

Quantum combs and testers entail a new paradigm of quantum information processing where the input of transformations and measurements are quantum
channels rather then states. In this talk, I will present two applications of this paradigm. The first application is the optimal automated learning of an unknown qubit unitary from a finite training set of N examples. The examples
are first exploited in an optimal storing network, whose output state is then sent to a retrieving machine that optimally reproduces the unknown unitary M times. The second application is the optimal alignment of reference frames with multiple rounds of quantum and classical communication. In this case, quantum combs and testers provide a simple proof that the maximum precision of reference frame alignment only depends on the total number of exchanged qubits,
and that a single round of forward quantum communication is sufficient to achieve it.