toqito.matrices.gen_gell_mann¶
Produces the generalized Gell-Mann operator matrices.
Module Contents¶
- toqito.matrices.gen_gell_mann.gen_gell_mann(ind_1, ind_2, dim)[source]¶
Produce a generalized Gell-Mann operator [@WikiGellMann].
Construct a dim-by-dim Hermitian operator. These matrices span the entire space of dim-by-dim matrices as ind_1 and ind_2 range from 0 to dim-1, inclusive, and they generalize the Pauli operators when dim = 2 and the Gell-Mann operators when dim = 3.
Examples
The generalized Gell-Mann matrix for ind_1 = 0, ind_2 = 1 and dim = 2 is given as
- [
- G_{0, 1, 2} = begin{pmatrix}
0 & 1 \ 1 & 0
end{pmatrix}.
]
This can be obtained in |toqito⟩ as follows.
```python exec=”1” source=”above” from toqito.matrices import gen_gell_mann
print(gen_gell_mann(ind_1=0, ind_2=1, dim=2)) ```
The generalized Gell-Mann matrix ind_1 = 2, ind_2 = 3, and dim = 4 is given as
- [
- G_{2, 3, 4} = begin{pmatrix}
0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 1 \ 0 & 0 & 1 & 0
end{pmatrix}.
]
This can be obtained in |toqito⟩ as follows.
```python exec=”1” source=”above” from toqito.matrices import gen_gell_mann
gen_gell_mann(ind_1=2, ind_2=3, dim=4) ```
- Parameters:
ind_1 (int) – A non-negative integer from 0 to dim-1 (inclusive).
ind_2 (int) – A non-negative integer from 0 to dim-1 (inclusive).
dim (int) – The dimension of the Gell-Mann operator.
- Returns:
The generalized Gell-Mann operator as an array.
- Return type:
numpy.ndarray