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Haha, yeah I mean a vector of the standard basis where one element is 1 and all others are 0. Does it make sense to measure in the standard basis if we can only measure eigenvalues though?
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
Terminology 
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.
CS bg, yes :D In quantum comp. people think of phi in C^(2^4) as storing amplitudes for each possible bit sequence 0000 0001 0010 etc. "Measuring in standard basis" samples e.g. 0010 with prob |phi_3|^2. Just curious how that works physically if you can only measure eigenvalues.
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