The Quantum Wasserstein Semidistance Is Not a Distance
Friedland and coauthors proposed a quantum analogue of the -Wasserstein distance and conjectured that, though only a semidistance in general, it is a true distance for a particular quantum cost matrix and for cost matrices near it. The paper disproves both conjectures with an explicit family of triples of states violating the triangle inequality.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Quantum Information, Optimal Transport
- Posed by
- Friedland, Eckstein, Cole and Życzkowski
- Year posed
- 2022
- Years open
- 4y
- Solved
- 2026-07-08
- Model
- ChatGPT 5
- Vendor
- OpenAI
- Collaborators
- Tomasz Miller
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The acknowledgements state the counterexamples were found with the assistance of ChatGPT 5.
Verification
No independent review, but the refutation is an explicit family of state triples and the triangle inequality can be checked directly. Preprint, not refereed.