What does the classical-shadow sample complexity depend on?

Question: A classical-shadow protocol is used to estimate M observables of an unknown quantum state. Which statement best reflects the standard theoretical guarantee? A) The required number of measurements is always independent of both system size and the selected observables B) The dependence on the number of target observables can be logarithmic in M, while the overall complexity also depends on the observables through quantities such as their shadow norms C) Exactly log₂(M) measurements are sufficient to estimate arbitrary observables with zero bias and fixed variance D) The protocol requires exponentially many measurements whenever any target observable is nonlocal Correct: B Explanation: Classical shadows can estimate many properties simultaneously with a logarithmic dependence on the number of requested properties. However, the prefactor depends on how difficult the chosen observables are to estimate under the measurement ensemble, so the result is not universally independent of system size or observable structure. Topic: advanced quantum computing / classical shadows / tomography