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arXiv · 1404.3035

Structure of the sets of mutually unbiased bases with cyclic symmetry

Ulrich Seyfarth·Luis L. Sanchez-Soto·Gerd Leuchs
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Abstract

Mutually unbiased bases that can be cyclically generated by a single unitary operator are of special interest, since they can be readily implemented in practice. We show that, for a system of qubits, finding such a generator can be cast as the problem of finding a symmetric matrix over the field $\mathbb{F}_2$ equipped with an irreducible characteristic polynomial of a given Fibonacci index. The entanglement structure of the resulting complete sets is determined by two additive matrices of the same size.

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Ulrich Seyfarth, Luis L. Sanchez-Soto, Gerd Leuchs. 2014-04-11. Structure of the sets of mutually unbiased bases with cyclic symmetry. https://doi.org/10.1088/1751-8113/47/45/455303

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