In Mermin's Quantum Computer Science, section 1.10 (Measurement gates and state preparation), Mermin writes that:

This role of measurement gates in state preparation follows from the Born rule if the Qbits that are to be prepared already have a state of their own, even though that state might not be known to the user of the quantum computer. It also follows from the generalized Born rule if the Qbits already share an entangled state – again, not necessarily known to the user – with additional (unmeasured) Qbits. But one cannot deduce from the Born rules that measurement gates serve to prepare states for Qbits “off the shelf,” whose past history nobody knows anything about. In such cases the use of measurement gates to assign a state to the Qbits is a reasonable and plausible extension of the Born rules. It is consistent with them, but goes beyond them.

Why are "off the shelf" qubits any different from qubits whose state is unknown to the user? And why does whatever property these qubits have mean that the use of measurement gates for state preperation doesn't follow directly from the Born rule?



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