We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two tractable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled nonlinear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results pave the way towards experimental investigations of fast scrambling and aspects of quantum gravity with quantum simulators.

中文翻译：

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快速加扰的最小模型

我们在具有长距离全部对所有和短距离相互作用的自旋模型中研究量子信息加扰。我们认为，简单的全局，空间上均匀的相互作用以及局部混沌动力学足以引起快速加扰，这说明了量子信息在整个系统中的传播时间是系统大小的对数。这在两个易于处理的模型中得到了说明：（1）具有Haar随机局部unit和全局相互作用的随机电路，以及（2）全局耦合非线性振荡器的经典模型。我们使用精确的数值通过研究无序的相关器的时间演化和中等大小的自旋链中的纠缠熵来提供进一步的证据。