bibkey: qiu2025multipartite authors: Xinyu Qiu; Zhiwei Song; Lin Chen year: 2025 title: “Multipartite entangling power by von Neumann entropy” doi: 10.1103/PhysRevA.111.022407 url: https://arxiv.org/abs/2410.15253v1 claim: “The entanglement generation K_{L:L^c}(U) of an n-partite unitary U is the supremum, over pure inputs psi_i of each party A_i with a local auxiliary system R_i, of the von Neumann entropy in ebits of the reduced state on L of U(psi_1 ⊗ … ⊗ psi_n); for the four-qubit Fredkin gate F_4 the paper shows K_{AD:BC}(F_4) ∈ [2, log_2 5] and conjectures K_{AD:BC}(F_4) = 2.” strata_touched:

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Multipartite entangling power by von Neumann entropy

X. Qiu, Z. Song and L. Chen, arXiv:2410.15253 (v1 2024-10-20, the only arXiv version); Phys. Rev. A 111, 022407 (2025). Subject: quant-ph.

The paper defines the entangling power of an n-partite unitary U_{A_1,…,A_n} as the supremum, over pure inputs ψ_i ∈ H_{A_iR_i} with local auxiliary systems R_i, of the largest von Neumann entropy across a bipartition L : L^c of U(ψ_1 ⊗ ⋯ ⊗ ψ_n) (Definition def:N-ep); for a fixed L the inner supremum is K_{L:L^c}(U). For the four-qubit Fredkin gate

F_4 = (|00⟩⟨00| + |01⟩⟨01| + |10⟩⟨10|)_{AB} ⊗ (I_2^{⊗2})_{CD} + |11⟩⟨11|_{AB} ⊗ (S_2)_{CD}

the paper computes K for the cuts A:BCD, C:ABD and AB:CD. For AD:BC it bounds K_{AD:BC}(F_4) below by 2, using the input |10⟩|10⟩|Φ⁺⟩|Φ⁺⟩, and above by log_2 5 via the Schmidt rank, and states:

Further we conjecture that $K_{AD:BC}(F_4)\le 2$ by numerical results and thus have the following. The entanglement generation $K_{AD:BC}(F_4)=2$. Hence the entangling power of a four-qubit Fredkin gate $F_4$ is equal to two ebits.

Verified locator

• DOI: https://doi.org/10.1103/PhysRevA.111.022407 (Crossref: published 2025-02-07). The APS abstract page repeats the arXiv abstract (“in two to log₂5 ebits”); the published full text was not read.
• URL: https://arxiv.org/abs/2410.15253v1 (source retrieved 2026-09-29): 20241020_entangling_power_xinyu.tex, Definition def:N-ep (l. 559–580), the gate F_4 (l. 1146–1152) and Conjecture coj:KAD:BC (l. 1184–1191).