Omanakuttan Sivaprasad, Lakshminarayan Arul
Center for Quantum Information and Control (CQuIC), Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA.
Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
Phys Rev E. 2021 Jan;103(1-1):012207. doi: 10.1103/PhysRevE.103.012207.
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.
利用简单的确定性动力系统作为硬币来研究造币离散时间量子行走，这些硬币的经典极限范围可以从可积到混沌。结果表明，类似洛施密特回波的保真度起着核心作用，当硬币是混沌的时候，这近似于经典随机游走者的特征函数。因此，经典二项分布作为量子行走的极限出现，并且游走者在最终变为弹道式之前表现出扩散增长。正如在多体局域化和耦合踢转子的情况下一样，硬币 - 游走者纠缠增长在时间上呈对数形式，并饱和到一个取决于硬币和游走者相对空间维度的值。在以硬币为主导的情形中，混沌可以使量子行走热化到典型的随机态，使得纠缠在哈尔平均佩奇值处饱和，这与以游走者为主导的情形不同，在后者中似乎会产生非典型态。
