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arXiv · 1909.07709

Entangling power of multipartite unitary gates

Tomasz Linowski·Grzegorz Rajchel-Mieldzioć·Karol Życzkowski
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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.

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Tomasz Linowski, Grzegorz Rajchel-Mieldzioć, Karol Życzkowski. 2019-09-17. Entangling power of multipartite unitary gates. https://doi.org/10.1088/1751-8121/ab749a

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