Multicomplementary operators via finite Fourier transform
摘要
A complete set of d+1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d+1 disjoint classes (each one having d-1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.
引用
@article{arxiv.quant-ph/0410155,
title = {Multicomplementary operators via finite Fourier transform},
author = {A. B. Klimov and L. L. Sanchez-Soto and H. de Guise},
journal= {arXiv preprint arXiv:quant-ph/0410155},
year = {2009}
}
备注
15 pages, no figures