= Solution
Yes, access to the original <qubits> can supply information about the secret encoding basis once the bit is known. For bit zero the possibilities are $|0\rangle$ and $|+\rangle$, whose overlap is $1/\sqrt2$; for bit one they are $|1\rangle$ and $|-\rangle$ with the same overlap magnitude. A <Helstrom measurement for two pure states> can identify which candidate was supplied more reliably than a blind basis guess. Measuring and preparing a state based on that evidence can improve an additional <known-bit quantum money forgery>[counterfeit], although the discrimination is not perfect and the <quantum measurement>[measurement] can disturb the original.
The <no-cloning theorem> rules out a deterministic perfect extra copy of both nonorthogonal candidates; it does not imply that access gives no advantage. The task of producing an additional accepted note should also be distinguished from simply returning the unaltered original, which already passes Alice's test. Requiring both the original and the extra note to survive imposes a further information-disturbance tradeoff.
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