toqito.random.random_ginibre

toqito.random.random_ginibre(dim_n, dim_m)[source]

Generate a Ginibre random matrix [WIKCIRC].

Generates a random dim_n-by-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 \(2\)-by-\(2\) 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 https://en.wikipedia.org/wiki/Circular_law

[HMN20]

Heinosaari, Teiko, Maria Anastasia Jivulescu, and Ion Nechita. “Random positive operator valued measures.” Journal of Mathematical Physics 61.4 (2020): 042202.

Parameters:

dim_n – The number of rows of the Ginibre random matrix.
dim_m – The number of columns of the Ginibre random matrix.

Returns:

A dim_n-by-dim_m Ginibre random density matrix.