pygsti.baseobjs.basisconstructors.gm_matrices

gm_matrices(matrix_dim)

Get the normalized elements of the generalized Gell-Mann basis with matrix dimension matrix_dim.

That is, construct the basis spanning the density-matrix space given by matrix_dim.

The returned matrices are given in the standard basis of the “embedding” density matrix space, that is, the space which embeds the block-diagonal matrix structure stipulated in matrix_dim. These matrices form an orthonormal basis under the trace inner product, i.e. Tr( dot(Mi,Mj) ) == delta_ij.

Parameters:

matrix_dim (int) – Dimension of the density-matrix space.

Returns:

A list of N numpy arrays each of shape (matrix_dim, matrix_dim), where matrix_dim is the matrix-dimension of the overall “embedding” density matrix (the sum of matrix_dim) and N is the dimension of the density-matrix space, equal to sum( block_dim_i^2 ).

Return type:

list