Entangling power of multipartite unitary gates

TL;DR

This paper investigates the entangling capabilities of multipartite unitary gates, deriving explicit formulas and analyzing their maximal entangling power, especially focusing on three-qubit systems and connections to maximally entangled states.

Contribution

It provides an analytical expression for the entangling power of n-partite gates and explores their properties in relation to maximally entangled states and average entangling power.

Findings

Derived an explicit formula for entangling power of n-partite gates.

Analyzed maximal entangling power and its relation to AME states.

Provided detailed analysis of three-qubit unitary and orthogonal gates.

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 $n$-partite Hilbert space of dimension $d_1 \ldots d_n$ to the entanglement of pure states in the Hilbert space of dimension $(d_1 \ldots d_n)^2$. 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 three-qubit unitary and orthogonal gates.