Yes we can solve this, for example, there is irreversible photochromic ink. Irreversible photochromic ink is a type of ink that changes color when exposed to UV light, but the color change is permanent and cannot be reversed, this can be used so paper bitcoin can trade hands but once someone scans and take it back to its wallet then it means that qr code no longer works.
That doesn't solve for the fact that someone or some information system has knowledge of the private key and has to have knowledge of the private key in order to record it on the note in the first place.
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