choi_to_pauli

choi_to_pauli(choi, order=1)

Convert a Choi-matrix to a Pauli-basis superoperator.

Note that this function assumes that the Choi-matrix is defined in the standard column-stacking convention and is normalized to have trace 1. For a channel E this is defined as: $choi = (I \otimes E)(bell_state)$.

The resulting ‘rauli’ R acts on input states as

where $|{\rho}\rangle =$ vectorize(rho, method='pauli') for order=1 and $|{\rho}\rangle =$ vectorize(rho, method='pauli_weights') for order=0.

Parameters

• choi (matrix) – the input Choi-matrix.
• order (int) – ordering of the Pauli group vector. order=1 (default) is standard lexicographic ordering (e.g. [II, IX, IY, IZ, XI, XX, XY,...]) order=0 is ordered by weights (e.g. [II, IX, IY, IZ, XI, XY, XZ, XX, XY,...])

Returns

A superoperator in the Pauli basis.

Return type

np.array