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

Kern, Oliver and Ranade, Kedar and Seyfarth, Ulrich (2010):
Complete sets of cyclic mutually unbiased bases in even prime-power dimensions.
In: J. Phys. A, pp. 5305--5321, 43, (27), DOI: 10.1088/1751-8113/43/27/275305,
[Article]

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 the 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 operators with the help of a suitable element of the Clifford group. As a consequence, we obtain complete sets of cyclic MUBs generated by a single element of the Clifford group in dimensions $2^m$ for $m=1,2,\dots,24$.

Item Type: Article
Erschienen: 2010
Creators: Kern, Oliver and Ranade, Kedar and Seyfarth, Ulrich
Title: Complete sets of cyclic mutually unbiased bases in even prime-power dimensions
Language: ["languages_typename_1" not defined]
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 the 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 operators with the help of a suitable element of the Clifford group. As a consequence, we obtain complete sets of cyclic MUBs generated by a single element of the Clifford group in dimensions $2^m$ for $m=1,2,\dots,24$.

Journal or Publication Title: J. Phys. A
Volume: 43
Number: 27
Uncontrolled Keywords: Secure Data
Divisions: LOEWE > LOEWE-Zentren > CASED – Center for Advanced Security Research Darmstadt
LOEWE > LOEWE-Zentren
LOEWE
Date Deposited: 30 Dec 2016 20:23
DOI: 10.1088/1751-8113/43/27/275305
Identification Number: TUD-CS-2010-0143
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