Source code for toqito.random.random_ginibre

"""Generate Ginibre random matrix."""
import numpy as np

[docs]def random_ginibre( dim_n: int, dim_m: int, ) -> np.ndarray: r""" Generate a Ginibre random matrix [WIKCIRC]_. Generates a random :code:`dim_n`-by-:code:`dim_m` Ginibre matrix. A *Ginibre random matrix* is a matrix with independent and identically distributed complex standard Gaussian entries. Ginibre random matrices are used in the construction of Wishart-random POVMs [HMN20]_. Examples ========== Generate a random :math:`2`-by-:math:`2` Ginibre random matrix. >>> from toqito.random import random_ginibre >>> random_ginibre(2, 2) [[ 0.06037649-0.05158031j 0.46797859+0.21872729j] [-0.95223112-0.71959831j 0.3404352 +0.11166238j]] References ========== .. [WIKCIRC] Wikipedia: Circular law .. [HMN20] Heinosaari, Teiko, Maria Anastasia Jivulescu, and Ion Nechita. "Random positive operator valued measures." Journal of Mathematical Physics 61.4 (2020): 042202. :param dim_n: The number of rows of the Ginibre random matrix. :param dim_m: The number of columns of the Ginibre random matrix. :return: A :code:`dim_n`-by-:code:`dim_m` Ginibre random density matrix. """ return (np.random.randn(dim_n, dim_m) + 1j * np.random.randn(dim_n, dim_m)) / np.sqrt(2)