A condition under which classical simulability implies efficient state learnability

Abstract: In the task of quantum state learning, one receives some data about measurements performed on a state, and using that, must make predictions on the outcomes of unseen measurements. Computing a prediction is generally hard but it has been shown that learning can be performed efficiently for states that are generated by Clifford circuits, which are known to be efficiently classically simulable. This naturally leads to the question, how does efficient state learnability compare with efficient classical simulation? In this work we introduce an extra condition on top of classical simulablity that guarantees efficiently learnability. To illustrate this we prove two new examples of efficient learnability: states with low (Schmidt rank) entanglement and states described by an 'efficient' ontological model.