Entanglement of local operators and the butterfly effect
Entanglement of local operators and the butterfly effect
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DOI：
10.1103/physrevresearch.3.033182
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发表时间：
2020-05
影响因子：
4.2
通讯作者：
Jonah Kudler-Flam;M. Nozaki;S. Ryu;Mao Tian Tan
中科院分区：
文献类型：
--
作者：
Jonah Kudler-Flam;M. Nozaki;S. Ryu;Mao Tian Tan
我们研究的鲁棒性的量子和经典信息的扰动实施本地运营商插入。我们这样做是通过计算多体纠缠措施在希尔伯特空间的本地运营商在海森堡图片。我们探索的对初始条件的敏感性是量子多体系统中蝴蝶效应的一个启发性表现。我们推导出一个“膜理论”在哈尔随机酉电路计算的互信息，对数负，并反映在当地运营商状态的熵映射到一个经典的统计力学问题，并发现任何本地运营商插入离域信息的速度是允许的因果关系。相同的行为被发现的共形场理论承认全息几何描述的整体几何是永恒的黑洞与一个本地对象位于视界。在可积系统中，如自由费米子和Clifford电路，只有$O（1）$量的信息被发现是离域的本地运营商。
We study the robustness of quantum and classical information to perturbations implemented by local operator insertions. We do this by computing multipartite entanglement measures in the Hilbert space of local operators in the Heisenberg picture. The sensitivity to initial conditions that we explore is an illuminating manifestation of the butterfly effect in quantum many-body systems. We derive a "membrane theory" in Haar random unitary circuits to compute the mutual information, logarithmic negativity, and reflected entropy in the local operator state by mapping to a classical statistical mechanics problem and find that any local operator insertion delocalizes information as fast as is allowed by causality. Identical behavior is found for conformal field theories admitting holographic duals where the bulk geometry is described by the eternal black hole with a local object situated at the horizon. In contrast to these maximal scramblers, only an $O(1)$ amount of information is found to be delocalized by local operators in integrable systems such as free fermions and Clifford circuits.