partial_trace

forest.benchmarking.operator_tools.calculational.partial_trace(rho, keep, dims, optimize=False)

Calculate the partial trace.

Consider a joint state ρ on the Hilbert space \(H_a \otimes H_b\). We wish to trace out \(H_b\)

\[ρ_a = Tr_b(ρ)\]

Parameters:

• rho – 2D array, the matrix to trace.
• keep – An array of indices of the spaces to keep after being traced. For instance, if the space is A x B x C x D and we want to trace out B and D, keep = [0, 2].
• dims – An array of the dimensions of each space. For example, if the space is A x B x C x D, dims = [dim_A, dim_B, dim_C, dim_D].
• optimize – optimize argument in einsum

Returns:

ρ_a, a 2D array i.e. the traced matrix