Entangling power of multipartite unitary 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 $d_1\dots d_n$ to the entanglement of pure states in the Hilbert space of dimension $(d_1\dots d_n{)}^2$. 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.

arXiv comment24 pages, 3 figures

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• Hierarchies among genuine multipartite entangling capabilities of quantum gates
• Tri-unitary quantum circuits
• Quantifying electron-nuclear spin entanglement dynamics in central-spin systems using one-tangles
• Absolutely maximally entangled pure states of multipartite quantum systems
• Imperfect Entangling Power of Quantum Gates