Werner 态纯化纠缠：规范纯化与非可加性

中文摘要 AI 辅助

我们证明了冯·诺依曼纯化纠缠是非可加性的。对于单重态权重 $1/64\le f\le1/4$ 的两量子比特 Werner 态 $W(f)$，我们展示了规范纯化是全局最优的：其纠缠，也称为反射熵，给出了精确的纯化纠缠。相反，对于 $0<f<f_\ast$（其中 $f_\ast\approx0.017$），正则化纯化纠缠严格低于反射熵。这些结果共同确立了在 $1/64\le f<f_\ast$ 范围内的非可加性。我们的规范最优性证明推广了文献 [1] 中的证明，该证明使用经典两量子比特态建立了 $0\le\alpha<1$ 时的 Rényi 非可加性。因此，我们解决了 $\alpha=1$ 时的可加性问题。值得注意的是，非可加性再次由可分离态见证，且底层态中不需要纠缠。

英文摘要

We prove that the von Neumann entanglement of purification is nonadditive. For two-qubit Werner states $W(f)$ with singlet weight $1/64\le f\le1/4$, we show that canonical purification is globally optimal: its entanglement, also known as reflected entropy, gives the exact entanglement of purification. In contrast, the regularized entanglement of purification lies strictly below the reflected entropy for $0<f<f_\ast$, where $f_\ast\approx0.017$. Together, these results establish nonadditivity throughout $1/64\le f<f_\ast$. Our canonical-optimality proof generalizes the proof in [1], which established Rényi nonadditivity for $0\leα<1$ using classical two-qubit states. We thus resolve the additivity question at $α=1$. Remarkably, nonadditivity is again witnessed by separable states and no entanglement in the underlying states is required.

发表机构

• Perimeter Institute for Theoretical Physics（Perimeter理论物理研究所）
• Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）

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