Numerical search for universal entanglers in C3⊗C4C3⊗C4 and C4⊗C4C4⊗C4

•It is presented a differential evolution-based algorithm that tests universal entanglers.•A separability criterion for pure C3⊗C4C3⊗C4 and C4⊗C4C4⊗C4 quantum states is presented.•Two good candidates to universal entanglers based on Pauli gates are provided.

A universal entangler is quantum gate able to transform any disentangled state into an entangled state. Although universal entanglers are abundant in arbitrary high dimensional spaces, to verify if a quantum gate is a universal entangler is a hard task since it is not known which property of the unitary matrix is responsible for such behavior. In this direction, the present work shows the results of an algorithm based on differential evolution that tests universal entanglers in C3⊗C4C3⊗C4 and C4⊗C4C4⊗C4. We present two good candidates for each cited space and we show that a candidate found in the literature is not a universal entangler.