MUB-10.3: Show that no single vector is mutually unbiased to any triple of three MU bases when d = 6.

← Open problems MUB-10.3

Blocked upstream

Show that no single vector is mutually unbiased to any triple of three MU bases when d = 6.

In plain terms

Strong unextendibility of triples. The review notes this would probably need an exhaustive classification of all MU triples.

Our position — ours alone, not the authors'

The vector-search half is exactly what our companion enumeration computes, and we would run it directly. The blocker is upstream: the exhaustive triple classification does not exist, and building it is Problem 10.5 plus Problem 10.4. We cannot start at the end of a chain whose first link is open.

Source

Daniel McNulty, Stefan Weigert, Mutually Unbiased Bases in Composite Dimensions -- A Review

Quantum 10, 2051 (2026) · §10.2
https://doi.org/10.22331/q-2026-04-01-2051
Licence: CC-BY-4.0 — the problem statement is quoted here under that licence, with attribution, and has not been modified