论文标题
与量子混沌硬币的量子步行：洛斯米特回声，经典限制和热化
Quantum walks with quantum chaotic coins: Of the Loschmidt echo, classical limit and thermalization
论文作者
论文摘要
使用简单的确定性动力学系统作为硬币研究了创建的离散时间量子步行，其经典限制可以从可集成到混乱。结果表明，像忠诚度这样的loschmidt回声起着核心作用，而当硬币混乱时，这大约是经典随机助行器的特征功能。因此，经典的二项式分布是作为量子步行的极限而产生的，并且步行者在最终变得弹道之前表现出扩散的生长。在多体定位和耦合的踢旋翼的情况下，硬币跟踪器的纠缠生长在时间上被证明是对数的，并且饱和到取决于相对硬币和沃克空间尺寸的值。在硬币主导的场景中，混乱可以将量子步行热量到典型的随机状态，从而使纠缠在HAAR平均页面值处饱和，这与在沃克主导的情况下似乎产生了非典型状态不同。
Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo like fidelity plays a central role and when the coin is chaotic this is approximately the characteristic function of a classical random walker. Thus the classical binomial distribution arises as a limit of the quantum walk and the walker exhibits diffusive growth before eventually becoming ballistic. The coin-walker entanglement growth is shown to be logarithmic in time as in the case of many-body localization and coupled kicked rotors, and saturates to a value that depends on the relative coin and walker space dimensions. In a coin dominated scenario, the chaos can thermalize the quantum walk to typical random states such that the entanglement saturates at the Haar averaged Page value, unlike in a walker dominated case when atypical states seem to be produced.
