Heisenberg–Weyl and Grossmann–Royer Operators

Patra, Saikat, Bihalan Bhattacharya

Heisenberg-Weyl operators provide a Hermitian generalization of Pauli operators in higher dimensions. Positive maps arising from Heisenberg-Weyl operators have been studied along with several algebraic and spectral properties of Heisenberg-Weyl observables. This allows to generalize the study of Pauli type maps in higher dimesional algebra of operators.

Leon W. Cohen

Man Wah Wong

We show in this chapter that localization operators on the Weyl-Heisenberg group are the same as the linear operators studied by Daubechies in the paper [12] on signal analysis. We begin with a detailed study of the Weyl-Heisenberg group.

Ali Asadian, Paul Erker, Marcus Huber +1 more

We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary density operator in discrete phase space, with a smooth transition to infinite dimensions. Furthermore, we derive bounds on the sum of expectation values of any set of anticommuting observables. Such bounds can be used in entanglement detection and we show that Heisenberg-Weyl observables provide a first nontrivial example beyond the dichotomic case.