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Structure of the sets of mutually unbiased bases with cyclic symmetry

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Seyfarth,  U.
Optics Theory Group, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Sanchez-Soto,  L. L.
Guests, Max Planck Institute for the Science of Light, Max Planck Society;

/persons/resource/persons201115

Leuchs,  G.
Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Citation

Seyfarth, U., Sanchez-Soto, L. L., & Leuchs, G. (2014). Structure of the sets of mutually unbiased bases with cyclic symmetry. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 47(45): 455303. doi:10.1088/1751-8113/47/45/455303.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-647C-F
Abstract
Mutually unbiased bases that can be cyclically generated by a single unitary operator are of special interest, for 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. 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.