Structure of the sets of mutually unbiased bases with cyclic symmetry

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.

20 pages

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Cited by in corpus (3)

• Galois Unitaries, Mutually Unbiased Bases, and MUB-balanced states
• Practical implementation of mutually unbiased bases using quantum circuits
• Cyclic measurements and simplified quantum state tomography