Compare Papers
Paper 1
The 27-qubit Counterexample to the LU-LC Conjecture is Minimal
Nathan Claudet
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.25219
- arXiv
- 2603.25219
It was once conjectured that two graph states are local unitary (LU) equivalent if and only if they are local Clifford (LC) equivalent. This so-called LU-LC conjecture was disproved in 2007, as a pair of 27-qubit graph states that are LU-equivalent, but not LC-equivalent, was discovered. We prove that this counterexample to the LU-LC conjecture is minimal. In other words, for graph states on up to 26 qubits, the notions of LU-equivalence and LC-equivalence coincide. This result is obtained by studying the structure of 2-local complementation, a special case of the recently introduced r-local complementation, and a generalization of the well-known local complementation. We make use of a connection with triorthogonal codes and Reed-Muller codes.
Open paperPaper 2
Operational meaning of the classical fidelity and the path length in Fisher-Kubo-Mori-Bogoliubov geometry
Lajos Diósi
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.04307
- arXiv
- 2410.04307
We show that the minimum entropy production in near-reversible quantum state transport along a path is simple function of the path length measured according to the Fisher-KMB metrics. Hence the sharp values of path lengths, also called statistical lengths, obtain operational meaning to quantify the residual irreversibility in near-reversible state transport. In the classical limit, the Bhattacharyya fidelity obtains a sharp operational meaning after eighty years.
Open paper