We study the entanglement structure of symmetry-protected topological (SPT) phases from an operational point of view by considering entanglement distillation in the presence of symmetries. We demonstrate that non-trivial SPT phases in one-dimension necessarily contain some entanglement which is inaccessible if the symmetry is enforced. More precisely, we consider the setting of local operations and classical communication (LOCC) where the local operations commute with a global onsite symmetry group G , which we call G -LOCC, and we define the inaccessible entanglement E inacc as the entanglement that cannot be used for distillation under G -LOCC. We derive a tight bound on E inacc which demonstrates a direct relation between inaccessible entanglement and the SPT phase, namely ##IMG## {$\mathrm{log}\left({D}_{\omega }^{2}\right){\leqslant}{E}_{\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{c}\mathrm{c}}{\leqslant}\mathr...}

中文翻译：

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在对称保护的拓扑阶段中无法访问的纠缠

我们从操作的角度，通过考虑对称性存在下的纠缠蒸馏来研究对称保护拓扑（SPT）相的纠缠结构。我们证明了一维非平凡的SPT相位必定包含一些纠缠，如果强制实施对称，则无法纠缠。更准确地说，我们考虑本地操作和经典通信（LOCC）的设置，其中本地操作与全局现场对称组G进行通信，我们称其为G -LOCC，并将不可访问的纠缠E inacc定义为无法纠缠的纠缠在G -LOCC下用于蒸馏。我们得出了E inacc的一个严格界限，它证明了不可接近的纠缠与SPT阶段之间的直接关系，