Abstract
It is known that mutually unbiased bases (MUBs), whenever they exist, are optimal in an information theoretic sense for the determination of the unknown state of a quantum ensemble. Such bases may not exist for most dimensions. The present paper deals with information gain in some generalizations and approximations of MUBs. We give estimates of the information loss (relative to MUBs) in these suboptimal choice of bases. For some generalization of MUBs we give exact calculations for the information gain. It is calculated directly in terms of transition probabilities among the measurement bases. We also give the formal solutions for the problem of quantum state tomography in these cases.
| Original language | English |
|---|---|
| Pages (from-to) | 10887-10902 |
| Number of pages | 16 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 40 |
| Issue number | 35 |
| DOIs | |
| Publication status | Published - 2007 |
Keywords
- Hilbert space
- distribution (probability theory)
- mathematical physics
- measure theory
- quantum computing
- quantum theory