Zhu, Huangjun (2017). Multiqubit Clifford groups are unitary 3-designs. Phys. Rev. A, 96 (6). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9934

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Abstract

Unitary t-designs are a ubiquitous tool in many research areas, including randomized benchmarking, quantum process tomography, and scrambling. Despite the intensive efforts of many researchers, little is known about unitary t-designs with t >= 3 in the literature. We show that the multiqubit Clifford group in any even prime-power dimension is not only a unitary 2-design, but also a 3-design. Moreover, it is a minimal 3-design except for dimension 4. As an immediate consequence, any orbit of pure states of the multiqubit Clifford group forms a complex projective 3-design; in particular, the set of stabilizer states forms a 3-design. In addition, our study is helpful in studying higher moments of the Clifford group, which are useful in many research areas ranging from quantum information science to signal processing. Furthermore, we reveal a surprising connection between unitary 3-designs and the physics of discrete phase spaces and thereby offer a simple explanation of why no discrete Wigner function is covariant with respect to the multiqubit Clifford group, which is of intrinsic interest in studying quantum computation.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Zhu, HuangjunUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-207626
DOI: 10.1103/PhysRevA.96.062336
Journal or Publication Title: Phys. Rev. A
Volume: 96
Number: 6
Date: 2017
Publisher: AMER PHYSICAL SOC
Place of Publication: COLLEGE PK
ISSN: 2469-9934
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
COMPLETE QUANTUM MEASUREMENTS; 2-DESIGNSMultiple languages
Optics; Physics, Atomic, Molecular & ChemicalMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/20762

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