rand.random_ginibre

Generate Ginibre random matrix.

Module Contents

Functions

random_ginibre(dim_n, dim_m)

Generate a Ginibre random matrix [1].
rand.random_ginibre.random_ginibre(dim_n, dim_m)

Generate a Ginibre random matrix [1].

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 [2].

Examples

Generate a random \(2\)-by-\(2\) Ginibre random matrix.

>>> from toqito.rand import random_ginibre
>>> random_ginibre(2, 2)
[[ 0.06037649-0.05158031j  0.46797859+0.21872729j]
 [-0.95223112-0.71959831j  0.3404352 +0.11166238j]]

References

[1] (1,2)

Wikipedia. Circular law. https://en.wikipedia.org/wiki/Circular_law.

[2]

Teiko Heinosaari, Maria Anastasia Jivulescu, and Ion Nechita. Random positive operator valued measures. Journal of Mathematical Physics, Apr 2020. URL: http://dx.doi.org/10.1063/1.5131028, doi:10.1063/1.5131028.

Parameters:

  • dim_n (int) – The number of rows of the Ginibre random matrix.

  • dim_m (int) – The number of columns of the Ginibre random matrix.

Returns:

A dim_n-by-dim_m Ginibre random density matrix.

Return type:

numpy.ndarray