## Nielsen and Chuang Exercise 2.62

Exercise 2.62Show that any measurement where the measurement operators and the POVM elements coincide is a projective measurement.

The POVM elements satisfy . The measurement operators satisfy . For these two operators to be the same, , which requires that . This is close to the definition of a projector, which is that . For the final component, we must show that the matrix is Hermitian, which it is if it is equivalent to the POVM elements. QED.

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