Constructing a Set of Kronecker-Pauli Matrices
Christian Rakotonirina · Qeios · 2024
In quantum physics, the choice of basis is crucial for formulation. The generalization of the Pauli matrices via Kronecker product, called Kronecker-Pauli matrices, is typically restricted to for \(2^n\) dimensional systems. This paper explores extending this generalization to \(N\)-dimensional systems, where \(N\) is a prime integer, in order to construct \(N\times N\)-Kronecker-Pauli matrices. We begin by examining the specific cases of \(3\times 3\) and \(5\times 5\) Kronecker-Pauli matrices, with the goal of the purpose constructing a set of \(N\times N\)-Kronecker-Pauli matrices for any prime integer \(N\).