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Aug 31, 2018 at 19:58 comment added DaftWullie @ahelwer no, because the measurement operators need not have rank 1. And eigenvalues are irrelevant in this case. The subscripts are arbitrary labels that you are free to pick. You are correct about the multi qubit measurement.
Aug 31, 2018 at 19:47 vote accept ahelwer
Aug 31, 2018 at 19:46 comment added ahelwer Thanks! Are the measurement operators $P_i$ always the outer product of the eigenvectors of the measurement observable, and subscripted with the eigenvalue? Also to clarify in the multi-qbit state, say to measure the middle qbit of a 3-qbit system $P_0$ would be $\mathbb{I}_2⊗|0\rangle\langle0|⊗\mathbb{I}_2$?
Aug 31, 2018 at 19:29 history edited DaftWullie CC BY-SA 4.0
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Aug 31, 2018 at 19:10 history answered DaftWullie CC BY-SA 4.0