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by whatshisface 858 days ago
The measurement operators are matrices that come about as a result of assigning real eigenvalues (these are your possible measurement outcomes) to orthonormal vectors (your arbitrary coordinate system). The results are hermitian, complex-valued matrices, because that's just what comes out if you try to engineer a matrix to have those eigenvalues and vectors. The rest follows from that.

Trying to fit a real number constraint somewhere, other than the one that's already there (real measurement outcomes), to me seems like the step you would have to justify, not the absence of one.
1 comments
MichaelZuo 858 days ago
Can you elaborate on the physical meaning that follows?

I just don't see how it links up with something tangible in the real world.

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whatshisface 858 days ago
The complex numbers in the matrices appear as a consequence of trying to do something else. I don't think they have much physical meaning on their own, which is why I am surprised that people ask what it would mean if they had to all be real numbers.
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MichaelZuo 858 days ago
The parent 'sw1sh' didn't ask that? Do you mean some sort of critique found elsewhere?
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