Multipartite Entanglement in Stabilizer Tensor Networks.
Multipartite Entanglement in Stabilizer Tensor Networks.
复制标题
稳定张量网络中的多部分纠缠。
DOI：
10.1103/physrevlett.125.241602
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发表时间：
2016
影响因子：
8.6
通讯作者：
M. Walter
中科院分区：
文献类型：
--
作者：
Sepehr Nezami;M. Walter
尽管量子纠缠在多体系统中具有根本的重要性，但我们的理解主要限于两体情况。事实上，即使是定义适当的多体纠缠概念，对一般量子系统来说也是一个重大挑战。在这项工作中，我们开始研究多体纠缠在一个丰富的，但易于处理的一类量子态称为稳定张量网络。我们证明了，对于一般的稳定张量网络，张量网络的几何形状通知状态的多体纠缠结构。特别是，我们表明，格林伯格-霍恩-蔡林格（GHZ）的三元组，可以从一个稳定张量网络的平均数量是小的，这意味着三方纠缠是稀缺的。这反过来又限制了态的更高粒子纠缠结构。最近的量子引力研究发现，稳定张量网络再现了AdS/CFT对应的重要结构特征，包括纠缠熵的Ryu-Takayanagi公式和某些量子纠错性质。我们的研究结果意味着一个新的业务解释的一夫一妻制的Ryu-Takayanagi互信息和熵诊断更高的部分纠缠。我们的技术贡献包括用于评估稳定张量网络的平均GHZ含量的自旋模型，以及随机稳定状态的三阶矩的新公式，我们希望在量子信息中找到进一步的应用。
Despite the fundamental importance of quantum entanglement in many-body systems, our understanding is mostly limited to bipartite situations. Indeed, even defining appropriate notions of multipartite entanglement is a significant challenge for general quantum systems. In this work, we initiate the study of multipartite entanglement in a rich, yet tractable class of quantum states called stabilizer tensor networks. We demonstrate that, for generic stabilizer tensor networks, the geometry of the tensor network informs the multipartite entanglement structure of the state. In particular, we show that the average number of Greenberger-Horne-Zeilinger (GHZ) triples that can be extracted from a stabilizer tensor network is small, implying that tripartite entanglement is scarce. This, in turn, restricts the higher-partite entanglement structure of the states. Recent research in quantum gravity found that stabilizer tensor networks reproduce important structural features of the AdS/CFT correspondence, including the Ryu-Takayanagi formula for the entanglement entropy and certain quantum error correction properties. Our results imply a new operational interpretation of the monogamy of the Ryu-Takayanagi mutual information and an entropic diagnostic for higher-partite entanglement. Our technical contributions include a spin model for evaluating the average GHZ content of stabilizer tensor networks, as well as a novel formula for the third moment of random stabilizer states, which we expect to find further applications in quantum information.
影响因子：
5.4
作者：
Dong, Xi;Harlow, Daniel;Marolf, Donald
通讯作者：
Marolf, Donald