A1 Refereed original research article in a scientific journal
Maximally symmetric stabilizer MUBs in even prime-power dimensions
Authors: Carmeli C, Schultz J, Toigo A
Publisher: AMER INST PHYSICS
Publication year: 2017
Journal: Journal of Mathematical Physics
Journal name in source: JOURNAL OF MATHEMATICAL PHYSICS
Journal acronym: J MATH PHYS
Article number: ARTN 032201
Volume: 58
Issue: 3
Number of pages: 17
ISSN: 0022-2488
eISSN: 1089-7658
DOI: https://doi.org/10.1063/1.4977830(external)
Abstract
One way to construct a maximal set of mutually unbiased bases (MUBs) in a primepower dimensional Hilbert space is by means of finite phase-space methods. MUBs obtained in this way are covariant with respect to some subgroup of the group of all affine symplectic phase-space transformations. However, this construction is not canonical: as a consequence, many different choices of covariance subgroups are possible. In particular, when the Hilbert space is 2(n) dimensional, it is known that covariance with respect to the full group of affine symplectic phase-space transformations can never be achieved. Here we show that in this case there exist two essentially different choices of maximal subgroups admitting covariant MUBs. For both of them, we explicitly construct a family of 2(n) covariant MUBs. We thus prove that, contrary to the odd dimensional case, maximally covariant MUBs are very far from being unique in even prime- power dimensions. Published by AIP Publishing.
One way to construct a maximal set of mutually unbiased bases (MUBs) in a primepower dimensional Hilbert space is by means of finite phase-space methods. MUBs obtained in this way are covariant with respect to some subgroup of the group of all affine symplectic phase-space transformations. However, this construction is not canonical: as a consequence, many different choices of covariance subgroups are possible. In particular, when the Hilbert space is 2(n) dimensional, it is known that covariance with respect to the full group of affine symplectic phase-space transformations can never be achieved. Here we show that in this case there exist two essentially different choices of maximal subgroups admitting covariant MUBs. For both of them, we explicitly construct a family of 2(n) covariant MUBs. We thus prove that, contrary to the odd dimensional case, maximally covariant MUBs are very far from being unique in even prime- power dimensions. Published by AIP Publishing.
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