Entangling power of multipartite unitary gates

Abstract

Abstract We study the entangling properties of multipartite unitary gates with respect to the measure of entanglement called one-tangle. Putting special emphasis on the case of three parties, we derive an analytical expression for the entangling power of an n-partite gate as an explicit function of the gate, linking the entangling power of gates acting on the n-partite Hilbert space of dimension to the entanglement of pure states in the Hilbert space of dimension . Furthermore, we evaluate its mean value averaged over the unitary and orthogonal groups, analyze the maximal entangling power and relate it to the absolutely maximally entangled (AME) states of a system with 2n parties. Finally, we provide a detailed analysis of the entangling properties of the three-qubit unitary and orthogonal gates.