ffsim.random.random_density_matrix

ffsim.random.random_density_matrix(dim, *, seed=None, dtype=<class 'complex'>)

Returns a random density matrix distributed with Hilbert-Schmidt measure.

A density matrix is positive semi-definite and has trace equal to one.

The Hilbert-Schmidt measure is the measure induced by tracing out one half of a uniformly random pure state on a doubled Hilbert space (see random_state_vector()). It is the canonical member of the family of induced measures: it is the flat measure on the set of density matrices, and it is invariant under conjugation by any unitary. If dtype is a real type, then the real analog is sampled instead.

Parameters:

• dim (int) – The width and height of the matrix.

• seed – A seed to initialize the pseudorandom number generator. Should be a valid input to np.random.default_rng.

• dtype – The data type to use for the result.

Return type:

ndarray

Returns:

The sampled density matrix.

Raises:

ValueError – Dimension must be at least one.

References

• Zyczkowski and Sommers, “Induced measures in the space of mixed quantum states” (2001)

• Osipov, Sommers, and Zyczkowski, “Random Bures mixed states and the distribution of their purity” (2010)