Integration over the Pauli quantum group

关于含赝费米子的动力学系统中的 2-qubit Pauli 群

On the Pauli group on 2-qubits in dynamical systems with pseudofermions

本文证明阶为16的 $P_1$ 和阶为64的 Pauli 2-群 $P_2$ 除量子计算外，也可出现在非自伴 Hamiltonians 描述的动力学系统中，从而允许用赝费米子算符表示它们。

Integration 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.

On the Quantum Lorentz Group

The quantum analogues of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indiceswe construct a quantum Minkowsky metric. In this framework, we show explicitely the correspondance between the SL(2,C) and Lorentz quantum groups.

Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions

The Groenewold-Moyal plane is the algebra A_θ(R^(d+1)) of functions on R^(d+1) with the star-product as the multiplication law, and the commutator [x_μ,x_ν] =i θ_{μν} between the coordinate functions. Chaichian et al. and Aschieri et al. have proved that the Poincare group acts as automorphisms on A_θ(R^(d+1))$ if the coproduct is deformed. (See also the prior work of Majid, Oeckl and Grosse et al). In fact, the diffeomorphism group with a deformed coproduct also does so according to the results of Aschieri et al. In this paper we show that for this new action, the Bose and Fermi commutation r…

Integration on algebraic quantum groupoids

In this article, we develop a theory of integration on algebraic quantum groupoids in the form of regular multiplier Hopf algebroids, and establish the main properties of integrals obtained by Van Daele for algebraic quantum groups before - faithfulness, uniqueness up to scaling, existence of a modular element and existence of a modular automorphism - for algebraic quantum groupoids under reasonable assumptions. The approach to integration developed in this article forms the basis for the extension of Pontrjagin duality to algebraic quantum groupoids, and for the passage from algebraic quantum…

可逆稳定化码的分类

A Classification of Invertible Stabilizer Codes

本文提出了一种基于相对L理论对可逆稳定化码进行分类的方法，并展示了其与二维拓扑秩序Witt群的同构关系。