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Suppose that we have a quantum state of the form:

$$|\psi\rangle = \sqrt{p}|0\rangle + \sqrt{1-p}|1\rangle$$

In order to get an estimate of the probability of reading $|0\rangle$ or $|1\rangle$, we need to sample $|\psi\rangle$. How many times do we need to sample to have an $\epsilon$-estimate ? Keep in mind that this is different from *quantum tomography* because i we don't want to reconstruct the state from measurements, i just want to find an approximation of the probability of reading some state. In Supervised Learning with Quantum Computers, Schuld,M, et.al, the authors say that sampling from a qubit is equivalent to sampling from a bernoulli distribution,thus we can use the Wald interval:

$$\epsilon = z\sqrt{{\bar{p}(1-\bar{p})}\over S}$$ where $z$ is the confidence level, $\bar{p}$ is the average and $S$ the number of samples.

In the case of $p$ being close to either 0 or 1, we can use Wilson Score interval:

$$
\epsilon = {z \over {1 + {z^2\over S}}}\sqrt{{{\bar{p}(1-\bar{p})}\over S} + {z^2 \over 4S^2}}
$$
Now, the i ask the following question: What if i have a state with multiple qubits? How do i get an $\epsilon$-estimate of the probability of reading some state? If you can suggest some references, i would appreciateit. Thank you very much.