Partial transpose (source code)

= Partial transpose
{title2=$\rho^{T_B}$}
{wiki}

In a fixed product basis, the partial transpose on subsystem $B$ sends
$$
|i\rangle\langle j|\otimes|k\rangle\langle\ell|
\longmapsto
|i\rangle\langle j|\otimes|\ell\rangle\langle k|.
$$
It preserves Hermiticity and trace but need not preserve positivity on entangled inputs.