The entanglement negativity and the positive partial-transpose criteria play important roles in quantifying the amount of entanglement for mixed states. Yet, because these measures generally involve partial transposing the density matrix w.r.t. some subsystem, which is not a CPTP map (though being hermitian-preserving), there is no straight way to implement it directly on a quantum computer. So my question is are there methods/quantum algorithms to implement the partial transposition of an input density matrix?
P.S.: the density matrix may be input using the block encoding techniques as show in this paper.