Partial trace (source code)

= Partial trace
{title2=$\operatorname{Tr}_B$}
{wiki}

The partial trace over $B$ is the linear operation characterized by
$$
\operatorname{Tr}[M_A\operatorname{Tr}_B(X_{AB})]
=\operatorname{Tr}[(M_A\otimes I_B)X_{AB}].
$$
Applied to a <density operator>, it produces a <reduced density matrix>.