Reduction criterion for separability

We introduce a separability criterion based on the positive map #:$ ̃(Tr $)!$ , where $ is a trace-class Hermitian operator. Any separable state is mapped by the tensor product of # and the identity into a nonnegative operator, which provides a simple necessary condition for separability. This condition is generally not sufficient because it is vulnerable to the dilution of entanglement. In the special case where one subsystem is a quantum bit, # reduces to time reversal, so that this separability condition is equivalent to partial transposition. It is therefore also sufficient for 2"2 and 2"3 systems. Finally, a simple connection between this map for two qubits and complex conjugation in the ‘‘magic’’ basis %Phys. Rev. Lett. 78, 5022 !1997"& is displayed. %S1050-2947!99"00708-8&