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I guess I’m just not sure what you mean by measure in the standard basis .. the measurement is a physical process and is basis independent and is represented by a unitary operator acting on the projective Hilbert space
Side effect of CS foundation is thinking in terms of data structures used to represent concepts in memory. In practice this means vectors always need a basis. In this case, a dot product can become a fast lookup if 𝜓 is represented using the operator's eigenvectors as a basis.
Can we make these vectors independent of basis? So that we can define any basis space whenever we want for these vectors in order to get output accordingly! These basis space may be a data structure, these vectors then gives components based on what data structure we impose!
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