连通楔是否意味着可蒸馏的纠缠？
Does connected wedge imply distillable entanglement?
AI总结：
本文研究了连通的纠缠楔是否意味着存在可蒸馏的纠缠，证明在主导阶次中不存在双分量纠缠，并通过局部可访问信息与纠缠楔横截面的关系，展示了可蒸馏纠缠的计算方法。
摘要：
Ryu-Takayanagi公式预测，即使两个边界子系统A和C在边界上是不连通的，并且被缓冲子系统B隔开，只要A和C在本征中具有连通的纠缠楔，它们仍可以表现出大的互信息I(A:C)。然而，减少的状态ρ_{AC}是否包含可蒸馏的EPR对一直是一个长期存在的开放问题。在本文中，我们通过证明以下两点来解决这个问题：i) 在G_N的主导阶次中没有LO可蒸馏的纠缠，这表明在全息混合态ρ_{AC}中没有双分量纠缠；ii) 一shot、一方向LOCC可蒸馏的纠缠在主导阶次中由局部可访问的信息J^W(A|C)给出，这与涉及（第三）纯化系统B的纠缠楔横截面E^W通过J^W(A|C) = S_A - E^W(A:B)相关。也就是说，我们证明了连通的纠缠楔并不一定意味着在一shot、一方向LOCC中存在非零的可蒸馏纠缠。我们还显示，纠缠形成E_F(A:C)在全息学主导阶次中由E^W(A:C)给出。
英文摘要：
The Ryu-Takayanagi formula predicts that two boundary subsystems $A$ and $C$ can exhibit large mutual information $I(A:C)$ even when they are spatially disconnected on the boundary and separated by a buffer subsystem $B$, as long as $A$ and $C$ have connected entanglement wedge in the bulk. However, whether the reduced state $ρ_{AC}$ contains distillable EPR pairs has remained a longstanding open problem. In this work, we resolve this problem by showing that: i) there is no LO-distillable entanglement at leading order in $G_N$, suggesting the absence of bipartite entanglement in a holographic mixed state $ρ_{AC}$, and ii) one-shot, one-way LOCC-distillable entanglement is given at leading order by locally accessible information $J^W(A|C)$, which is related to the entanglement wedge cross section $E^W$ involving the (third) purifying system $B$ via $J^W(A|C) = S_A - E^W(A:B)$. Namely, we demonstrate that a connected entanglement wedge does not necessarily imply nonzero distillable entanglement in one-shot, one-way LOCC. We also show that entanglement of formation $E_{F}(A:C)$ is given by $E^W(A:C)$ at leading order in holography.
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