Perfectly Complete Quantum Key Agreement from One-Way Functions
Whether perfectly complete quantum key agreement can be built from quantumly secure one-way functions in a black-box way. It cannot: for any protocol where Alice and Bob exchange only classical messages, make at most and quantum queries to a Boolean random oracle and agree on a key with certainty, an eavesdropper given the classical messages recovers the key with certainty in classical oracle queries, independent of the number of rounds and the transcript length.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Quantum cryptography
- Posed by
- —
- Year posed
- —
- Years open
- —
- Solved
- 2026-08-04
- Model
- GPT-5.6 Sol Ultra
- Vendor
- OpenAI
- Collaborators
- Longcheng Li, Qian Li, Xingjian Li, Qipeng Liu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The acknowledgment states that GPT-5.6 Sol Ultra discovered the proof in a one-shot conversation and produced a preliminary draft, with the authors independently verifying every statement and proof, then simplifying and refining the argument.
Verification
arXiv preprint, not yet peer-reviewed.
Source
arXiv:2608.03824 - Impossibility of Perfectly Complete Many-Round Key Agreement in the QROM