Zhu, Huangjun (2017). Multiqubit Clifford groups are unitary 3-designs. Phys. Rev. A, 96 (6). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9934
Full text not available from this repository.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: |
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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: |
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Refereed: | Yes | ||||||||
URI: | http://kups.ub.uni-koeln.de/id/eprint/20762 |
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