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I would like to ask some questions in regards to preparing mixed states.

Assuming I am allowed to prepary any pure quantum state, perform measurements and apply unitaries, I am asked to prepare a single qubit quantum state of maximum entropy.

As I understand, a 1-qubit quantum state of maximal entropy is one that gives 50/50 chance of either measurement, whatever the two orthonormal states I pick. So basically, randomly firing a pure state would do and I don't unitaries/measurements for this? Would also firing just two chosen orthonormal pure states also work? Or should I prepare a pure state 1/sqrt(2)|0>+1/sqrt(2)|1> and measure it with respect to basis |0> and |1>, then there's a 50/50 chance of the qubit being either |0> or |1>, i.e. exhibiting the same probabilities as the mixed state of maximal entropy would.