Universality of Weyl unitaries
نویسندگان
چکیده
Weyl's unitary matrices, which were introduced in 1927 paper [12] on group theory and quantum mechanics, are p × matrices given by the diagonal matrix whose entries -th roots of unity cyclic shift matrix. unitaries, we denote u v , satisfy = 1 (the identity matrix) commutation relation ζ where is a primitive root unity. We prove that universal following sense: if any d such then there exists unital completely positive linear map ϕ : M ( C ) → . also show, moreover, two pairs order Weyl equivalent, but assertion for three unitaries fails. There standard tensor-product construction involving Pauli produces irreducible sequences anticommuting selfadjoint arbitrary length. The this sequence called Weyl-Brauer [11, Definition 6.63] This generalised herein to case ≥ 3 producing call matrices. show as g -tuple, extremal their range, using recent ideas from noncommutative convexity theory.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2022
ISSN: ['1873-1856', '0024-3795']
DOI: https://doi.org/10.1016/j.laa.2021.10.017