Learning quantum processes without input control

Understand

We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state.

• Our setting is motivated by the practical situation in which one desires to learn a quantum process governed by classical parameters that are out of one's control.
• This framework is applicable, for example, to the study of astronomical phenomena, disordered systems and biological processes not controlled by the observer.
• We provide an algorithm for learning with high probability in this setting with a finite amount of samples, even if the concept class is infinite.