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arXiv 2502.04437quant-phhep-th
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三party 零散态没有双party 纠缠

Tripartite Haar random state has no bipartite entanglement

IBM Quantum（IBM量子）；National Research Council Canada（加拿大国家研究委员会）；Perimeter Institute for Theoretical Physics（基础物理前沿研究所）；Department of Physics, Rikkyo University（立教大学物理学系）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）

Zhi Li, Takato Mori, Beni Yoshida

备注：
(v1) 14 pages, 5 figures; (v2) an author (Zhi Li) added. Improved bounds with new results on local operation distillation and logical operators; (v3) Added Sections 1.2.4 and 5 discussing generalizations, Section 1.4 for intuitions of the proofs, a comment in relation to QFT entanglement in Section 6.1, and an additional comment in Section 7. 36 pages, 5 figures
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AI总结：

该研究证明了在三party 零散态中，无法通过局部单元操作或局部操作提取EPR-like双party 纠缠，并给出了在给定EPR保真度容忍度下采样具有EPR-like纠缠态的概率上限，显示了纠缠态数量的双指数抑制。此外，该研究还建立了三party 纠缠在Haar随机态中的结构约束，表明W-或GHZ-like纠缠无法被提取，并且不存在非平凡的全局对称性。最后，该研究讨论了AdS/CFT对应中的一物理解释，指出连接的纠缠楔不一定意味着双party 纠缠，这与之前的信念相悖。

摘要：

我们证明，从三party Haar随机态|Ψ⟩_{ABC}中，无法通过局部单元操作或局部操作提取EPR-like双party纠缠，当每个子系统A、B或C的qubit数量少于总qubit数量的一半时。具体而言，我们推导了在给定EPR保真度容忍度下采样具有EPR-like纠缠态的概率上限，显示了纠缠态数量的双指数抑制。我们的证明依赖于一个简单的体积论证，补充了ε-网论证和集中测度。将|Ψ⟩_{ABC}视为双party量子纠错码C→AB，这表明输出子系统A或B不支持任何非平凡的逻辑算子。我们还建立了三party纠缠在Haar随机态中的结构约束，表明W-或GHZ-like纠缠无法被提取，并且不存在非平凡的全局对称性。最后，我们讨论了AdS/CFT对应中的一个物理解释，指出连接的纠缠楔不一定意味着双party纠缠，这与之前的信念相悖。

英文摘要：

We show that no EPR-like bipartite entanglement can be distilled from a tripartite Haar random state $|Ψ\rangle_{ABC}$ by local unitaries or local operations when each subsystem $A$, $B$, or $C$ has fewer than half of the total qubits. Specifically, we derive an upper bound on the probability of sampling a state with EPR-like entanglement at a given EPR fidelity tolerance, showing a doubly-exponential suppression in the number of qubits. Our proof relies on a simple volume argument supplemented by an $ε$-net argument and concentration of measure. Viewing $|Ψ\rangle_{ABC}$ as a bipartite quantum error-correcting code $C\to AB$, this implies that neither output subsystem $A$ nor $B$ supports any non-trivial logical operator. We also establish general constraints on the structure of tripartite entanglement in Haar random states, showing that W- or GHZ-like entanglement cannot be distilled and that nontrivial global symmetries are absent. Finally, we discuss a physical interpretation in the AdS/CFT correspondence, indicating that a connected entanglement wedge does not necessarily imply bipartite entanglement, contrary to a previous belief.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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