纠缠幂动力学：遍历性与混合性
Entangling Power Dynamics: Ergodicity and Mixing
浏览论文内容
中文总结 AI 辅助
该研究以纠缠幂为框架，建立了动力学的遍历层级，发现两量子比特幺正门既非遍历也非混合，受激伊辛链中可积与非可积多体系统的遍历性、混合性表现存在差异，还引入类Lyapunov指数表征收敛速率。
中文摘要 AI 辅助
我们从纠缠产生的视角研究量子动力学，通过含时纠缠幂所留下的不同特征来表征 underlying 的幺正演化。对于一个幺正算符，我们将其遍历性表征为长时间平均纠缠幂与Haar平均线性熵相等；我们更严格地将混合性定义为含时纠缠幂本身在长时间收敛到Haar值。在该框架内，我们建立了动力学行为的遍历层级，特别表明混合性蕴含遍历性，但遍历性不一定蕴含混合性。作为应用，我们发现两量子比特幺正门既非遍历也非混合：其长时间平均纠缠幂仅能取四个离散值，无一同Haar平均值重合。随后我们用受激伊辛链研究多体动力学，发现可积与非可积情形下，长时间平均纠缠幂均收敛到Haar值，表明存在遍历性；但值得注意的是，非可积链表现出混合性，而可积链虽具遍历性却明显非混合。我们还引入类Lyapunov指数来表征含时纠缠幂趋近饱和值的速率，发现该指数随多体系统中可积性破缺程度的增加而系统增大。我们的结果确立了纠缠产生是表征动力学系统的有用框架，并揭示了超越传统诊断的可积性的定性不同特征。
英文摘要
We study quantum dynamics through the lens of entanglement generation and characterize the underlying unitary evolution by the distinct signatures it imprints on the time-dependent entangling power. For a unitary operator, we characterize ergodicity by the equality between its long-time-averaged entangling power and the Haar-averaged linear entropy. We define mixing more stringently as the convergence of the time-dependent entangling power itself to the Haar value at long times. Within this framework, we establish the ergodic hierarchy of dynamical behavior, showing in particular that mixing implies ergodicity, whereas ergodicity does not necessarily imply mixing. As an application, we find that two-qubit unitary gates are neither ergodic nor mixing: their long-time-averaged entangling power can take only four discrete values, none of which coincides with the Haar average. We then investigate many-body dynamics using the kicked Ising chain and find that the long-time-averaged entangling power converges to the Haar value in both integrable and nonintegrable cases, indicating ergodicity. Remarkably, however, the nonintegrable chain exhibits mixing, whereas the integrable chain, despite being ergodic, is demonstrably nonmixing. We also introduce a Lyapunov-like exponent to characterize the rate at which the time-dependent entangling power approaches its saturation value. We find that this exponent increases systematically with the degree of integrability breaking in the many-body system. Our results establish entanglement generation as a useful framework for characterizing dynamical systems and reveal qualitatively different signatures of integrability beyond conventional diagnostics.
