Physics – Quantum Physics
Scientific paper
2005-11-25
Journal of Physics A: Mathematical and General 39 (2006) 1669-1682
Physics
Quantum Physics
15 pages, 3 figures; displayed abstract is shortened, see the paper for the complete abstract
Scientific paper
10.1088/0305-4470/39/7/011
Weyl's displacement operators for position and momentum commute if the product of the elementary displacements equals Planck's constant. Then, their common eigenstates constitute the Zak basis, each state specified by two phase parameters. Upon enforcing a periodic dependence on the phases, one gets a one-to-one mapping of the Hilbert space on the line onto the Hilbert space on the torus. The Fourier coefficients of the periodic Zak bases make up the discrete Zak bases. The two bases are mutually unbiased. We study these bases in detail, including a brief discussion of their relation to Aharonov's modular operators, and mention how they can be used to associate with the single degree of freedom of the line a pair of genuine qubits.
Englert Berthold-Georg
Lee Kean Loon
Mann Ady
Revzen Michael
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