SIC-POVMs and mutually unbiased bases
A quantum measurement can be built from a set of equally spaced states, the quantum analogue of a perfectly symmetric arrangement of points on a sphere. Whether such sets exist in every dimension, and how many mutually unbiased bases (measurement bases where knowing one outcome tells nothing about the others) exist in dimension 6, are unsolved.
Why it matters
These objects give optimal schemes for state reconstruction and cryptography and are tied to deep questions in number theory.
Review
P. Horodecki, L. Rudnicki and K. Zyczkowski, Five open problems in quantum information theory, PRX Quantum, 2022. https://arxiv.org/abs/2002.03233 reference checked
Timestamp record
- Signed record
- 1bdfc0d09903…
- Public log
- Entry 346, in checkpoint 2,123
- In the log by
- Block 969,698, 2026-10-03
This text was in the PubPhys log by that date. The date says nothing about when the problem was first posed.