用于仅测量纠缠相变的经典元胞自动机
Classical Cellular Automaton for Measurement-Only Entanglement Transitions
- Western Washington University（西华盛顿大学）
- Advanced Materials Science and Engineering Center, Western Washington University（西华盛顿大学先进材料科学与工程中心）
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种经典长程随机元胞自动机，精确模拟仅测量量子系统的纠缠相变，发现体积律、分形律和面积律三种区域，并避免了轨迹后选择的指数成本。
AI中文摘要：
我们引入了一种广义的经典长程随机元胞自动机，它精确地捕捉了仅测量监控量子系统的纠缠动力学和相变。相应的量子模型由一维量子比特链组成，该链受到竞争性的单点和长程贝尔测量的作用，其中间隔距离服从幂律分布。在每条轨迹的每一步，态保持为贝尔对和未配对量子比特的张量积，双分纠缠熵完全编码在站点的一个经典匹配中。这种精确表示使我们能够在若干极限下解析地求解动力学，并确定纠缠熵的稳态标度。我们发现体积律、分形律和面积律三种区域。数值结果表明，这些区域在解析可解极限之外仍然存在。由于贝尔测量结果只影响贝尔态标签而不影响匹配，所有子系统熵与测量结果无关，从而避免了轨迹后选择的指数成本。
英文摘要：
We introduce a generalized classical long-range stochastic cellular automaton that exactly captures the entanglement dynamics and transitions of a measurement-only monitored quantum system. The corresponding quantum model consists of a one-dimensional qubit chain subject to competing single-site and long-range Bell measurements, with separations drawn from a power-law distribution. At every step of each trajectory, the state remains a tensor product of Bell pairs and unpaired qubits, with bipartite entanglement entropy fully encoded in a classical matching of the sites. This exact representation allows us to solve the dynamics analytically in several limits and to determine the steady-state scaling of the entanglement entropy. We find volume-law, fractal, and area-law regimes. Numerical results show that these regimes persist beyond the analytically solvable limit. Because Bell outcomes affect only Bell-state labels and not the matching, all subsystem entropies are outcome independent, avoiding the exponential cost of trajectory postselection.
