Scholarlink

<p>The Ryu-Takayanagi formula predicts that two boundary subsystems <i>A</i> and <i>C</i> can exhibit large mutual information <i>I</i>(<i>A</i> : <i>C</i>) even when they are spatially disconnected on the boundary and separated by a buffer subsystem <i>B</i>, as long as <i>A</i> and <i>C</i> have connected entanglement wedge in the bulk. However, whether the reduced state <i>ρ</i><sub><i>AC</i></sub> 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 <i>G</i><sub><i>N</i></sub>, suggesting the absence of bipartite entanglement in a holographic mixed state <i>ρ</i><sub><i>AC</i></sub>, and ii) one-shot, one-way LOCC-distillable entanglement is given at leading order by locally accessible information <i>J</i><sup><i>W</i></sup>(<i>A</i>|<i>C</i>), which is related to the entanglement wedge cross section <i>E</i><sup><i>W</i></sup> involving the (third) purifying system <i>B</i> via <i>J</i><sup><i>W</i></sup>(<i>A</i>|<i>C</i>) = <i>S</i><sub><i>A</i></sub> − <i>E</i><sup><i>W</i></sup> (<i>A</i> : <i>B</i>). 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 <i>E</i><sub><i>F</i></sub>(<i>A</i> : <i>C</i>) is given by <i>E</i><sup><i>W</i></sup>(<i>A</i> : <i>C</i>) at leading order in holography.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Does connected wedge imply distillable entanglement?

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月19日

查看全文
  • Takato Mori,
  • Beni Yoshida

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 ρAC 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 GN, suggesting the absence of bipartite entanglement in a holographic mixed state ρAC, and ii) one-shot, one-way LOCC-distillable entanglement is given at leading order by locally accessible information JW(A|C), which is related to the entanglement wedge cross section EW involving the (third) purifying system B via JW(A|C) = SA − EW (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 EF(A : C) is given by EW(A : C) at leading order in holography.