Path-Finding, Orbit State Preparation, and the Security of Invariant Quantum Money
The paper argues invariant quantum money security hinges on a falsifiable state-preparation assumption, not path-finding alone.
The paper examines when path-finding hardness is the right assumption for knot-based and invariant quantum money. Existing proofs add unfalsifiable knowledge-of-path assumptions; for group orbits that can be superposed, average-case path-finding hardness is necessary, but for knots a path-finder only reduces forgery to state preparation. The authors propose a falsifiable preparation assumption that, together with a transfer assumption, is equivalent to security against forgers that measure first, and show no fully black-box reduction derives transfer from preparation alone.
- Path-finding alone does not prove security of invariant quantum money.
- Knowledge-of-path assumptions are unfalsifiable and not known to follow from security.
- For knots, a path-finder only reduces forgery to state preparation.
- Preparation plus a transfer assumption match security against measure-first forgers.
From the original article
1 min read at arxiv.orgThe security of quantum money from knots, and of its generalization to invariant money, is based on the assumption that path-finding, exhibiting a sequence of moves between two equivalent objects, is hard. No proof of security from that assumption alone is known.
By Hans Schmiedel · arxiv.org
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