A2 Vertaisarvioitu katsausartikkeli tieteellisessä lehdessä
Covariant mutually unbiased bases
Tekijät: Carmeli C, Schultz J, Toigo A
Kustantaja: WORLD SCIENTIFIC PUBL CO PTE LTD
Julkaisuvuosi: 2016
Journal: Reviews in Mathematical Physics
Tietokannassa oleva lehden nimi: REVIEWS IN MATHEMATICAL PHYSICS
Lehden akronyymi: REV MATH PHYS
Artikkelin numero: ARTN 1650009
Vuosikerta: 28
Numero: 4
Sivujen määrä: 43
ISSN: 0129-055X
eISSN: 1793-6659
DOI: https://doi.org/10.1142/S0129055X16500094
Tiivistelmä
The connection between maximal sets of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space and finite phase-space geometries is well known. In this article, we classify MUBs according to their degree of covariance with respect to the natural symmetries of a finite phase-space, which are the group of its affine symplectic transformations. We prove that there exist maximal sets of MUBs that are covariant with respect to the full group only in odd prime-power dimensional spaces, and in this case, their equivalence class is actually unique. Despite this limitation, we show that in dimension 2(r) covariance can still be achieved by restricting to proper subgroups of the symplectic group, that constitute the finite analogues of the oscillator group. For these subgroups, we explicitly construct the unitary operators yielding the covariance.
The connection between maximal sets of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space and finite phase-space geometries is well known. In this article, we classify MUBs according to their degree of covariance with respect to the natural symmetries of a finite phase-space, which are the group of its affine symplectic transformations. We prove that there exist maximal sets of MUBs that are covariant with respect to the full group only in odd prime-power dimensional spaces, and in this case, their equivalence class is actually unique. Despite this limitation, we show that in dimension 2(r) covariance can still be achieved by restricting to proper subgroups of the symplectic group, that constitute the finite analogues of the oscillator group. For these subgroups, we explicitly construct the unitary operators yielding the covariance.
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