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Consider a source emits states [itex]|\Phi\rangle = \cos\theta |0\rangle + e^{i\phi}\sin\theta |1\rangle[/itex] with fixed [itex]\theta[/itex] and random phases [itex]\phi[/itex], with equal probability for each phase.

How can I show that a measurement of the operator Z ([itex]Z|0\rangle = |0\rangle , Z|1\rangle = -|1\rangle[/itex]) doesn't yield any information about the state emitted by the source?