A trapped-ion qubit is prepared and measured times in the computational basis

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Quantum Information and Technology, Ch What a qubit must do: requirements, tomography and benchmarking

Problem

A trapped-ion qubit is prepared and measured 750750 times in the computational basis. The outcome ∣0⟩|0\rangle is recorded 690690 times. ((a)) Write the log-likelihood of this record as a function of the unknown probability p0=P(∣0⟩)p_0 = P(|0\rangle). ((b)) Find the maximum-likelihood estimate p^0\hat p_0 and its standard error.

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