Complete sets of cyclic mutually unbiased bases in even prime power dimensions

Abstract

We present a construction method for complete sets of cyclic mutually unbiased bases (MUBs) in Hilbert spaces of even prime power dimensions. In comparison to usual complete sets of MUBs, complete cyclic sets possess the additional property of being generated by a single unitary operator. The construction method is based on the idea of obtaining a partition of multi-qubit Pauli operators into maximal commuting sets of orthogonal operators with the help of a suitable element of the Clifford group. As a consequence, we explicitly obtain complete sets of cyclic MUBs generated by a single element of the Clifford group in dimensions $2^m$ for $m=1,2,...,24$.

10 pages

References in corpus (2)

• Mubs and Hadamards of Order Six
• Generation of mutually unbiased bases as powers of a unitary matrix in 2-power dimensions

Cited by in corpus (11)

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• Construction of mutually unbiased bases with cyclic symmetry for qubit systems
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• States that "look the same" with respect to every basis in a mutually unbiased set
• Systems of Imprimitivity for the Clifford Group
• Structure of the sets of mutually unbiased bases with cyclic symmetry
• Cyclic Mutually Unbiased Bases and Quantum Public-Key Encryption
• Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture
• Studies of symmetries that give special quantum states the "right to exist"
• Practical implementation of mutually unbiased bases using quantum circuits
• Cyclic measurements and simplified quantum state tomography