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arXiv · 0708.4114

Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions

P. Sulc·J. Tolar
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Abstract

Mutually unbiased bases in Hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity. An alternative proof of existence of a maximal collection of N+1 mutually unbiased bases in Hilbert spaces of prime dimension N is given by exploiting the finite Heisenberg group (also called the Pauli group) and the action of SL(2,Z_N) on finite phase space Z_N x Z_N implemented by unitary operators in the Hilbert space. Crucial for the proof is that, for prime N, Z_N is also a finite field.

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P. Sulc, J. Tolar. 2007-11-05. Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions. https://doi.org/10.1088/1751-8113%2F40%2F50%2F013

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