منابع مشابه
Integration over the Pauli Quantum Group
The notion of free quantum group appeared in Wang’s papers [17], [18]. The idea is that given a compact group G ⊂ Un, the matrix coordinates uij ∈ C(G) commute with each other, and satisfy certain relations R. One can define then the universal algebra A generated by abstract variables uij, subject to the relations R. In certain situations we get a Hopf algebra in the sense of Woronowicz [20], a...
متن کاملIntegration over Compact Quantum Groups
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures. Introduction A basic question in functional analysis is to find axioms for quantum groups, which ensure the existence of a Haar measure. In the compact case, this ...
متن کاملIntegration over Quantum Permutation Groups
A remarkable fact, discovered by Wang in [14], is that the set Xn = {1, . . . , n} has a quantum permutation group. For n = 1, 2, 3 this is the usual symmetric group Sn. However, starting from n = 4 the situation is different: for instance the dual of Z2 ∗ Z2 acts on X4. In other words, “quantum permutations” do exist. They form a compact quantum group Qn, satisfying the axioms of Woronowicz in...
متن کاملInvariant Integration over the Unitary Group
Integrals for the product of unitary-matrix elements over the U (n) group will be discussed. A group-theoretical formula is available to convert them into a multiple sum, but unfortunately the sums are often tedious to compute. In this paper, we develop an alternative method in which these sums are avoided, and group theory is rendered unnecessary. Only unitarity and the invariance of the Haar ...
متن کاملTwelve-dimensional Pauli group contextuality
The goal of the paper is to check whether the real eigenstates of the observables in the single qudit Pauli group may lead to quantum contextuality, the property that mutually compatible and independent experiments depend on each other. We find that quantum contextuality crops up at dimension twelve in various configurations with a few rays. We use the Shannon capacity for characterizing the co...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2008
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2008.03.002