In quantum physics, the choice of basis is crucial for formulation. The generalization of the Pauli matrices via the Kronecker product, known as Pauli strings, is typically restricted to $2^{n}$ dimensional systems. This paper explores extending this generalization to $N$ -dimensional systems, where $N$ is a prime integer, 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 $N$ . Another possible method for constructing a set of Kronecker-Pauli matrices is discussed.In quantum physics, the choice of basis is crucial for formulation. The generalization of the Pauli matrices via the Kronecker product, known as Pauli strings, is typically restricted to $2^{n}$ dimensional systems. This paper explores extending this generalization to $N$-dimensional systems, where $N$ is a prime integer, 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 $N$. Another possible method for constructing a set of Kronecker-Pauli matrices is discussed.

QeiosAug 9, 20250 citations

Constructing a Set of Kronecker-Pauli Matrices

Christian Rakotonirina

In quantum physics, the choice of basis is crucial for formulation. The generalization of the Pauli matrices via the Kronecker product, known as Pauli strings, is typically restricted to $2^{n}$ dimensional systems. This paper explores extending this generalization to $N$ -dimensional systems, where $N$ is a prime integer, 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 $N$ .In quantum physics, the choice of basis is crucial for formulation. The generalization of the Pauli matrices via the Kronecker product, known as Pauli strings, is typically restricted to $2^{n}$ dimensional systems. This paper explores extending this generalization to $N$-dimensional systems, where $N$ is a prime integer, 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 $N$.

QeiosMar 14, 20250 citations

Constructing a Set of Kronecker-Pauli Matrices

Christian Rakotonirina

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 $N$ .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 $N$.

QeiosOct 18, 20242 citations

Constructing a Set of Kronecker-Pauli Matrices

Christian Rakotonirina

QeiosSep 20, 20241 citation

A Relation Between the Chrestenson Operator, Weyl Operator Basis, and Kronecker-Pauli Operator Basis

Mickaya A. Razanaparany, Christian Rakotonirina

Within the framework of quantum theory, we review the Chrestenson operator, the Weyl operator basis, and the Kronecker-Pauli operator basis in $d$ -dimensional Hilbert spaces using Dirac notation, where $d$ is a prime integer strictly greater than 2. We establish a new algebraic relation connecting these operators and present the cases $d=3$ and $d=5$ as illustrative examples.Within the framework of quantum theory, we review the Chrestenson operator, the Weyl operator basis, and the Kronecker-Pauli operator basis in $d$-dimensional Hilbert spaces using Dirac notation, where $d$ is a prime integer strictly greater than 2. We establish a new algebraic relation connecting these operators and present the cases $d=3$ and $d=5$ as illustrative examples.

quant-pharXiv:2602.19573Feb 24, 20260 citations

Kronecker-Pauli Operators

Christian Rakotonirina

In quantum mechanics, classical matrix bases such as the Pauli matrices are often generalized to higher dimensions. So, it is useful to express their corresponding operators using the Dirac Bra and Ket. In this paper, to express the corresponding operators we review the Kronecker-Pauli matrices and how to construct them for an N-dimensional system, with N a prime integer, N>2. Then, we give the expression of the Kronecker-Pauli operators and show that their matrices with respect to the standard basis fulfill the conditions to form a set of Kronecker-Pauli matrices. Relationship between the Kronecker-Pauli operators and the Weyl operators has been studied.In quantum mechanics, classical matrix bases such as the Pauli matrices are often generalized to higher dimensions. So, it is useful to express their corresponding operators using the Dirac Bra and Ket. In this paper, to express the corresponding operators we review the Kronecker-Pauli matrices and how to construct them for an N-dimensional system, with N a prime integer, N>2. Then, we give the expression of the Kronecker-Pauli operators and show that their matrices with respect to the standard basis fulfill the conditions to form a set of Kronecker-Pauli matrices. Relationship between the Kronecker-Pauli operators and the Weyl operators has been studied.

QeiosAug 9, 20250 citations

In quantum physics, the choice of basis is crucial for formulation. The generalization of the Pauli matrices via the Kronecker product, known as Pauli strings, is typically restricted to

2^{n}

dimensional systems. This paper explores extending this generalization to

N

-dimensional systems, where

N

is a prime integer, 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

. Another possible method for constructing a set of Kronecker-Pauli matrices is discussed.

In quantum physics, the choice of basis is crucial for formulation. The generalization of the Pauli matrices via the Kronecker product, known as Pauli strings, is typically restricted to

2^{n}

dimensional systems. This paper explores extending this generalization to

N

-dimensional systems, where

N

is a prime integer, 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

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

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

Within the framework of quantum theory, we review the Chrestenson operator, the Weyl operator basis, and the Kronecker-Pauli operator basis in

d

-dimensional Hilbert spaces using Dirac notation, where

d

is a prime integer strictly greater than 2. We establish a new algebraic relation connecting these operators and present the cases

d=3

and

d=5

as illustrative examples.