Geometrical approach to mutually unbiased bases

Details Geometrical approach to mutually unbiased bases Geometrical approach to mutually unbiased bases

2007-06-18

arxiv.org/abs/0706.2626v1

J. Phys. A 40, 3987 (2007)

Physics

Quantum Physics

10 pages. Some typos in the journal version have been corrected

Scientific paper

10.1088/1751-8113/40/14/014

We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We also consider the feasible transformations between different kinds of curves and show that they correspond to local rotations around the Bloch-sphere principal axes. We suggest how to generalize the method to systems in dimensions that are powers of a prime.

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