发表机构
Princeton University; Massachusetts Institute of Technology（普林斯顿大学; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在Floquet监测Clifford电路中证明纠缠与纯化转变可分离，引入逻辑支持半径和逻辑Krylov维数，揭示体积律与面积律相变及新普适类。
AI 中文摘要
纠缠转变可以在没有相应纯化转变的情况下发生。我们在每个Floquet周期具有固定层数的空间局域监测Clifford电路中证明了这种分离，其中Clifford门和Pauli测量的空间随机模式在时间上精确重复。在这种重复下，稀有的空间结构持续存在，并打破了传统时空随机电路中所发现的纠缠与纯化之间的对应关系。在一维空间中，初始乘积态产生的晚期纠缠保持面积律，而如果初始态是最大混合态，系统在热力学极限和长时间极限下仍保持广泛混合。在二维或更高维度中，我们发现了体积律与面积律纠缠之间的转变，而系统在该转变的两侧均保持混合。在这两种相中，大量的量子信息无限期地存活，并且尽管有重复测量，仍进行幺正演化。我们引入逻辑支持半径来表征其空间扩展，并将体积律和面积律相分别与离域和局域逻辑动力学相关联。我们进一步引入逻辑Krylov维数，它统计从初始局域算子动态生成的独立逻辑算子的数量。其标度解决了转变问题，并为测量诱导相变的新普适类提供了证据。
英文摘要
An entanglement transition can occur without a corresponding transition in purification. We demonstrate this separation in spatially local monitored Clifford circuits with a fixed number of layers per Floquet period, where a spatially random pattern of Clifford gates and Pauli measurements is repeated exactly in time. Rare spatial structures persist under this repetition and break the correspondence between entanglement and purification found in conventional spacetime-random circuits. In one spatial dimension, the late-time entanglement produced with an initial product state remains area-law, while the system remains extensively mixed in the thermodynamic and long-time limits if the initial state is maximally mixed. In two or more dimensions, we find a transition between volume-law and area-law entanglement while the system remains mixed on both sides of this transition. An extensive amount of quantum information survives indefinitely in both phases and evolves unitarily despite the repeated measurements. We introduce the logical-support radius to characterize its spatial spreading and identify the volume-law and area-law phases with delocalized and localized logical dynamics, respectively. We further introduce the logical Krylov dimension, which counts the independent logical operators dynamically generated from an initially local operator. Its scaling resolves the transition and provides evidence for a new universality class of measurement-induced phase transitions.
Comments21 pages, 14 figures
