标题： 从量子遍历性中增强的纠缠 显示英文标题

标题： Enhanced entanglement from quantum ergodicity

摘要： 量子混沌猜想将量子系统的光谱统计与量子遍历性的抽象概念联系起来。 这种关联被认为是量子混沌的基本且有时是定义性的，但其实际相关性受到了理论和实验发展的挑战。 在此，我们表明，遍历动力学可以直接用于制备比由最大混杂电路（如随机单元）生成的量子态具有更高参数纠缠度的量子态。 我们的设置涉及通过守恒电荷的“非破坏性”相互作用耦合的量子系统。 我们推导出初始乘积态的演化纠缠与该状态下相互作用电荷的光谱统计量之间的精确关系。 这种联系通过一个与量子动力学随时间生成正交态的能力相关的Krylov向量遍历性概念来解释。 我们考虑利用这一现象在复杂系统之间制备近似的爱因斯坦-波多尔斯基-罗森（EPR）态，这是诸如量子隐形传态等任务的关键资源。 我们定量地展示了，作为EPR态效用基础的纠缠系统之间的算子传递，可以通过遍历动力学生成的纠缠具有更大的参数容量，而不是通过最大混杂。 我们的分析表明，“遍历”光谱统计量可直接应用于量子信息任务作为一种潜在的资源。 显示英文摘要

摘要： The quantum chaos conjecture associates the spectral statistics of a quantum system with abstract notions of quantum ergodicity. Such associations are taken to be of fundamental and sometimes defining importance for quantum chaos, but their practical relevance has been challenged by theoretical and experimental developments. Here, in counterpoint, we show that ergodic dynamics can be directly utilized for the preparation of quantum states with parametrically higher entanglement than generated by maximally scrambling circuits such as random unitaries. Our setting involves quantum systems coupled via a "non-demolition" interaction of conserved charges. We derive an exact relation between the evolving entanglement of an initial product state and a measure of spectral statistics of the interacting charges in this state. This connection is explained via a notion of Krylov vector ergodicity, tied to the ability of quantum dynamics to generate orthonormal states over time. We consider exploiting this phenomenon for the preparation of approximate Einstein-Podolsky-Rosen (EPR) states between complex systems, a crucial resource for tasks such as quantum teleportation. We quantitatively show that the transfer of operators between entangled systems, which underlies the utility of the EPR state, can be performed with parametrically larger capacity for entanglement generated via ergodic dynamics than with maximal scrambling. Our analysis suggests a direct application of "ergodic" spectral statistics as a potential resource for quantum information tasks.