dq.sdissipator

sdissipator(L: ArrayLike) -> Array

Returns the Lindblad dissipation superoperator (in matrix form).

The dissipation superoperator \(\mathcal{D}[L]\) is defined by: $$ \mathcal{D}[L] (\rho) = L\rho L^\dag - \frac{1}{2}L^\dag L \rho - \frac{1}{2}\rho L^\dag L. $$

The vectorized form of this superoperator is: $$ L^* \otimes L - \frac{1}{2} (I_n \otimes L^\dag L) - \frac{1}{2} (L^\mathrm{T} L^* \otimes I_n). $$

Parameters

• L (array_like of shape (..., n, n)) –

  Jump operator.

Returns

(array of shape (..., n^2, n^2)) Dissipation superoperator.

See also

• dq.dissipator(): applies the dissipation superoperator to a state using only \(n\times n\) matrix multiplications.