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

TL;DR

This paper introduces a method to construct complete cyclic sets of mutually unbiased bases in even prime power dimensions, generated by a single unitary operator, using Clifford group elements.

Contribution

The paper provides an explicit construction of complete cyclic MUBs in dimensions 2^m for m=1 to 24, advancing the understanding of MUB structures in quantum information.

Findings

Constructed complete cyclic MUBs in dimensions up to 2^24

Utilized Clifford group elements to generate MUBs

Enhanced the framework for quantum state measurement and quantum cryptography

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 $m=1,2,...,24$.