toqito.matrix_props.is_rank_one¶

Checks if a matrix has rank one.

Module Contents¶

toqito.matrix_props.is_rank_one.is_rank_one(mat, tol=1e-08)[source]¶

Determine whether the given matrix has rank one [@WikiMatrixRank].

The function evaluates the singular values (equivalently, eigenvalues for Hermitian matrices) and counts how many are greater than the provided tolerance.

Examples

Consider the Bell state density matrix (rho = ket{Phi^+}bra{Phi^+}). This matrix has rank one.

```python exec=”1” source=”above” from toqito.matrix_props import is_rank_one from toqito.states import bell

rho = bell(0) @ bell(0).conj().T print(is_rank_one(rho)) ```

On the other hand, the maximally mixed state is not rank one.

```python exec=”1” source=”above” import numpy as np from toqito.matrix_props import is_rank_one

maximally_mixed = np.eye(2) / 2 print(is_rank_one(maximally_mixed)) ```

Parameters:

mat (numpy.ndarray) – Matrix to test.
tol (float) – Numerical tolerance used when distinguishing non-zero singular values.

Returns:

True if the matrix has rank at most one, False otherwise.

Return type:

bool