"We now consider measurements of A and B when they are compatible observables. Suppose we measure A first and obtain result a'. Subsequently, we may measure B and get result b'. Finally we measure A again. It follows from our measurement formalism that the third measurement always gives a' with certainty; that is, the second (B) measurement does not destroy the previous information obtained in the first (A) measurement. This is rather obvious when the eigenvalues of A are nondegenerate:|\alpha \rangle \xrightarrow{\text{A measurement}} |a', b' \rangle \xrightarrow{\text{B measurement}} |a', b' \rangle \xrightarrow{\text{A measurement}} |a', b' \rangle."
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Original Language: English
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J. J. Sakurai and Jim J. Napolitano, Modern Quantum Mechanics (2nd ed., 2011)
https://en.wikiquote.org/wiki/Measurement_in_quantum_mechanics
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Measurement in quantum mechanics
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