What is the key limitation of classical shadows?

Question: Classical shadows can estimate many observables from randomized measurements. Which statement gives the most accurate limitation? A) Their sample complexity can be logarithmic in the number of observables, but still depends strongly on the measurement ensemble and the observables' shadow norms B) They exactly reconstruct the density matrix with polynomial samples for every arbitrary quantum state C) They require the observables to be chosen before measurement, otherwise the guarantee fails D) They work only for product states and cannot estimate entangled observables Correct: A Explanation: Classical shadows are powerful because the same randomized measurement data can be reused for many target properties. But the difficulty of estimating a property depends on the observable and measurement scheme; the logarithmic dependence on the number of observables is not the whole cost. Topic: advanced quantum computing / classical shadows / tomography