W Siegel’s research while affiliated with Stony Brook University and other places

... Few paragraphs down I shall draw a distinction between measurement and observation 6 Operator is perfectly able to distinguish orthogonal inputs , , since ⟨ | | ⟩ = 0. It's just not able to encode its output as classical information, because output of is the same for any input: ⟨ | | ⟩ = ⟨ | | ⟩ = 1. The informationproducing measurement can only be performed by operator whose output is different for different inputs 7 A competed measurement event, e.g., a click of a particle detector, implicitly includes [29] 8 Sometimes it is incorrectly stated [19] that is "do nothing" operator 9 Also called the fundamental representation [30] 10 Trace of a product of two Hermitian operators is always real ...

Reference:

Dimensionality of observable space