论文标题
量子蜂窝自动机，张量网络和区域定律
Quantum Cellular Automata, Tensor Networks, and Area Laws
论文作者
论文摘要
量子细胞自动机是保留位置和尊重因果关系的统一图。我们在任何维度上都通过简单的张量网络（PEPU）识别它们，其键尺寸不会随系统大小而增长。结果，他们满足了可以创建的纠缠熵的区域法律。我们定义了其他类别的非单身地图，即所谓的量子通道，即尊重因果关系或保留地方。我们表明，尽管后者遵守了一个区域法律，因为他们可以创建的量子相关量，如量子互信息所衡量的，但前者可能会违反它。我们还表明，它们都不能表示为具有独立于系统大小的键尺寸的张量网络。
Quantum Cellular Automata are unitary maps that preserve locality and respect causality. We identify them, in any dimension, with simple tensor networks (PEPU) whose bond dimension does not grow with the system size. As a result, they satisfy an area law for the entanglement entropy they can create. We define other classes of non-unitary maps, the so-called quantum channels, that either respect causality or preserve locality. We show that, whereas the latter obey an area law for the amount of quantum correlations they can create, as measured by the quantum mutual information, the former may violate it. We also show that neither of them can be expressed as tensor networks with a bond dimension that is independent of the system size.
