Mutually unbiased bases for continuous variables
Abstract
The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For N=2 , the golden ratio occurs in the definition of these mutually unbiased bases suggesting the relevance of number theory not only in the finite-dimensional setting.
- Publication:
-
Physical Review A
- Pub Date:
- August 2008
- DOI:
- arXiv:
- arXiv:0802.0394
- Bibcode:
- 2008PhRvA..78b0303W
- Keywords:
-
- 03.65.Ca;
- 03.65.Ta;
- 42.50.Dv;
- Formalism;
- Foundations of quantum mechanics;
- measurement theory;
- Nonclassical states of the electromagnetic field including entangled photon states;
- quantum state engineering and measurements;
- Quantum Physics
- E-Print:
- 5 pages, no figures, revised to be identical to published text