ginibre_matrix_complex

forest.benchmarking.operator_tools.random_operators.ginibre_matrix_complex(dim: int, k: int, rs: Optional[mtrand.RandomState] = None) → numpy.ndarray

Given a scalars dim and k, returns a dim by k matrix, drawn from the complex Ginibre ensemble [IM].

Each element is distributed

\[\sim [N(0, 1) + i · N(0, 1)]\]

Here \(X \sim N(0,1)\) denotes a normally distributed random variable.

[IM]	Induced measures in the space of mixed quantum states. Zyczkowski et al. J. Phys A: Math. and Gen. 34, 7111 (2001). https://doi.org/10.1088/0305-4470/34/35/335 https://arxiv.org/abs/quant-ph/0012101

Parameters:

• dim – Hilbert space dimension.
• k – Ultimately becomes the rank of a state.
• rs – Optional random state.

Returns:

Returns a dim by k matrix, drawn from the Ginibre ensemble.