Question: For 2x2 and 2x3 systems, is the partial transpose the only positive but not completely positive operation that is possible?
Why this came up: The criteria for detecting if a state $\rho$ is entangled is:
$\forall \Lambda $ such that $\Lambda$ is a positive but not completely positive operator, if $$(I \otimes \Lambda ) \rho \geq 0 $$ then the state is separable, otherwise it is entangled.
However, we know the Peres-Horodecki criteria for 2x2 and 2x3 systems says it is enough to check only for one positive operation, that is, the partial transpose. Hence I was wondering if this was true.