论文标题
测量引起的纠缠相位转变
Measurement-Induced Entanglement Phase Transition in Random Bilocal Circuits
论文作者
论文摘要
近年来，已经在各种随机电路模型中研究了由纠缠统一动力学和分解投影测量之间的竞争引起的测量引起的纠缠相变。在本文中，我们研究了一个简单的$ n $ qudit brownian电路模型的平均纯度动力学，并具有全面的随机交互和测量。在很大的限制中，我们的模型在半古典限制中映射到一维量子链，这使我们能够分析模型的关键行为和其他各种属性。我们表明，长期以来，由总系统熵的行为区分了两个阶段。另外，这两个阶段还具有不同的子系统熵行为。低测量率阶段在第二雷尼熵与子系统大小的行为中具有第一衍生的不连续性，类似于随机状态的“页面曲线”，而另一阶段的熵曲线平滑。
Measurement-induced entanglement phase transitions, caused by the competition between entangling unitary dynamics and disentangling projective measurements, have been studied in various random circuit models in recent years. In this paper, we study the dynamics of averaged purity for a simple $N$-qudit Brownian circuit model with all-to-all random interaction and measurements. In the large-$N$ limit, our model is mapped to a one-dimensional quantum chain in the semi-classical limit, which allows us to analytically study critical behaviors and various other properties of the model. We show that there are two phases distinguished by the behavior of the total system entropy in the long time. In addition, the two phases also have distinct subsystem entropy behavior. The low measurement rate phase has a first-derivative discontinuity in the behavior of second Renyi entropy versus subsystem size, similar to the "Page curve" of a random state, while the other phase has a smooth entropy curve.
