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

Abstract

The group of matrices $P_1$ of Pauli is a finite 2-group of order 16 and plays a fundamental role in quantum information theory, since it is related to the quantum information on the 1-qubit. Here we show that both $P_1$ and the Pauli 2-group $P_2$ of order 64 on 2-qubits, other than in quantum computing, can also appear in dynamical systems which are described by non self-adjoint Hamiltonians. This will allow us to represent $P_1$ and $P_2$ in terms of pseudofermionic operators.

Version of December 2022; 12pp; accepted for publication in Forum Math. after changes due to the report

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Fermionic coherent states for pseudo-Hermitian two-level systems
• Variations on a theme of Heisenberg, Pauli and Weyl