Entanglement spread area law in gapped ground states
Entanglement spread area law in gapped ground states
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DOI：
10.1038/s41567-022-01740-7
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发表时间：
2020-04
期刊：
影响因子：
19.6
通讯作者：
Anurag Anshu;A. Harrow;Mehdi Soleimanifar
中科院分区：
文献类型：
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作者：
Anurag Anshu;A. Harrow;Mehdi Soleimanifar
基态纠缠控制着低温下量子多体系统的各种性质，是理解物质的带隙量子相的关键。在这里，我们确定了一个结构性的纠缠在基态的带隙局部哈密顿量。这种性质是使用称为纠缠扩散的量子信息量捕获的，它测量了雷尼纠缠熵之间的差异。我们的主要结果表明，带隙基态具有有限的纠缠传播在任何分区的系统，表现出面积律标度。我们的结果适用于任何图形描述的相互作用的系统，但我们得到了一个改进的界限格的特殊情况。这些相互作用图包括已知纠缠熵不满足面积定律的情况。我们首先通过将基态纠缠与测试二分纠缠态的通信复杂性联系起来，然后使用最近开发的用于Hamilton模拟的量子算法设计一种测试基态的通信方案来实现我们的结果。
Ground-state entanglement governs various properties of quantum many-body systems at low temperatures and is the key to understanding gapped quantum phases of matter. Here we identify a structural property of entanglement in the ground state of gapped local Hamiltonians. This property is captured using a quantum information quantity known as the entanglement spread, which measures the difference between Rényi entanglement entropies. Our main result shows that gapped ground states possess limited entanglement spread across any partition of the system, exhibiting an area-law scaling. Our result applies to systems with interactions described by any graph, but we obtain an improved bound for the special case of lattices. These interaction graphs include cases where entanglement entropy is known not to satisfy an area law. We achieve our results first by connecting the ground-state entanglement to the communication complexity of testing bipartite entangled states and then devising a communication scheme for testing ground states using recently developed quantum algorithms for Hamiltonian simulation.