Entangling characterization ofSWAP1∕mand controlled unitary gates

Abstract

We study the entangling power and perfect entangler nature of ${\mathrm{SWAP}}^{1∕m}$ for $m\ensuremath{\geqslant}1$ and controlled-unitary (CU) gates. It is shown that ${\mathrm{SWAP}}^{1∕2}$ is the only perfect entangler in the ${\mathrm{SWAP}}^{1∕m}$ family. On the other hand, a subset of CU gates which is locally equivalent to controlled-NOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.