论文标题
动态纯化和投影集合的量子状态设计的出现
Dynamical purification and the emergence of quantum state designs from the projected ensemble
论文作者
论文摘要
多体系统中的量子热化是由局部子系统朝着通用形式的方法定义的，可以描述为量子状态的合奏，其中可观察到可观察到的热期望值。最近，证明这些量子状态的分布也可以表现出普遍的统计数据，而将每个状态与互补子系统的局部投影测量结果相关联。具体而言，在某些条件下，这种纯量子状态的集合可以模仿最大熵，均匀随机的合奏的行为，即形成一个{\ it量子状态设计}，代表一种``更深的''形式的量子热化形式。在这项工作中，我们研究了这种新颖的新兴普遍性的动态过程。利用时空二元映射到一维量子电路时，我们认为在受监视的量子系统的背景下产生的动态纯化物理学限制了投影的集合对均匀分布的方法。我们证明，在时空双重动力学（在具有适当初始状态和最终测量碱基的双重量子电路中实现的条件和最终测量库）中，通常会在所有时刻$ k $同时产生精确的状态设计，从而扩展了先前的严格结果[HO和Choi，ho and choi，ho and choi，ho and choi。莱特牧师。 {\ bf 128}，060601（2022）]。相反，我们表明，与这些条件相比，动态纯化可以导致分离时间表之间的时间表，以矩量$ k = 1 $（常规的热化）与高矩$ k \ gg 1 $（深度热化）之间的量子状态设计之间的形成。我们的结果表明，投影的集合可以探测无法定期热化（例如量子信息争夺）无法访问的量子动力学特征。
Quantum thermalization in a many-body system is defined by the approach of local subsystems towards a universal form, describable as an ensemble of quantum states wherein observables acquire thermal expectation values. Recently, it was demonstrated that the distribution of these quantum states can also exhibit universal statistics, upon associating each state with the outcome of a local projective measurement of the complementary subsystem. Specifically, this collection of pure quantum states -- called the projected ensemble -- can under certain conditions mimic the behavior of a maximally entropic, uniformly random ensemble, i.e., form a {\it quantum state-design}, representing a ``deeper'' form of quantum thermalization. In this work, we investigate the dynamical process underlying this novel emergent universality. Leveraging a space-time duality mapping for one-dimensional quantum circuits, we argue that the physics of dynamical purification, which arises in the context of monitored quantum systems, constrains the the projected ensemble's approach towards the uniform distribution. We prove that absence of dynamical purification in the space-time dual dynamics (a condition realized in dual-unitary quantum circuits with appropriate initial states and final measurement bases) generically yields exact state-designs for all moments $k$ at the same time, extending previous rigorous results [Ho and Choi, Phys. Rev. Lett. {\bf 128}, 060601 (2022)]. Conversely, we show that, departing from these conditions, dynamical purification can lead to a separation of timescales between the formation of a quantum state-design for moment $k=1$ (regular thermalization) and for high moments $k\gg 1$ (deep thermalization). Our results suggest that the projected ensemble can probe nuanced features of quantum dynamics inaccessible to regular thermalization, such as quantum information scrambling.
