Abstract
An analytic proof is given which shows that it is impossible to extend any triple of mutually unbiased (MU) product bases in dimension six by a single MU vector. Furthermore, the 16 states obtained by removing two orthogonal states from any MU product triple cannot figure in a (hypothetical) complete set of seven MU bases. These results follow from exploiting the structure of MU product bases in a novel fashion, and they are among the strongest ones obtained for MU bases in dimension six without recourse to computer algebra.
| Original language | English |
|---|---|
| Article number | 1250056 |
| Number of pages | 12 |
| Journal | INTERNATIONAL JOURNAL OF QUANTUM INFORMATION |
| Volume | 10 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 11 Sept 2012 |
Keywords
- Quantum Physics (quant-ph)
- Mutually unbiased bases;
- complementarity;
- finite-dimensional quantum systems