High School Measurement postulate = von Neumann’s projection postulate?

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The discussion centers on the potential synonymy between the "measurement postulate" and "von Neumann’s projection postulate" in quantum mechanics. It highlights that while both terms are often used in literature, they are rarely mentioned together, leading to confusion about their meanings. The consensus is that the "measurement postulate" lacks a precise definition and, when referring to state changes during measurements, can be considered synonymous with the projection postulate. Additionally, distinctions between "von Neumann projection" and "Lüders projection" are noted, but these are deemed largely semantic. Ultimately, both terms are viewed as different names for the same underlying concept.
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I'm wondering if the "measurement postulate" and the "von Neumann’s projection postulate" refer to the same concept?
I find in the literature frequent reference to the "measurement postulate" and, sometimes, to the "von Neumann’s projection postulate". The difference, if any, seems to me subtle but I can't tell which. However, they are never mentioned both in the same context/paper, so I'm afraid that they may be two completely different postulates not to be confused. I don't get what the difference is. So, the question is if they are synonymous (in that case a simple "yes" answer is sufficient) or , if not, what distinguishes it?
 
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My impression is that "measurement postulate" is not a term with a well-defined meaning. If it is used to refer to the change of state during a textbook measurement, it is another name for the projection postulate, yes.

Sometimes, people distinguish between "von Neumann projection" and "Lüders projection" where the latter is used for projections on multidimensional subspaces in the presence of degeneracy but this is really just unimportant semantics.
 
They are synonmous, just two different names for the same thing. You'll even see Von Neumann's measurement postulate.
 
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