  The experimental evaluation of many quantum mechanical quantities requires
the estimation of several directly measurable observables, such as local
observables. Due to the necessity to repeat experiments on individual quantum
systems in order to estimate expectation values of observables, the question
arises how many repetitions to allocate to a given directly measurable
observable. We show that an active learning scheme can help to improve such
allocations, and the resultant decrease in experimental repetitions required to
evaluate a quantity with the desired accuracy increases with the size of the
underlying quantum mechanical system.
