空间中的测量诱导相变
Measurement-induced phase transition in space
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中文总结 AI 辅助
研究通过在单个受监测的 Clifford 链中施加确定性测量梯度实现测量诱导相变的空间实现，利用扫描纠缠可观测量表明相变由空间标度形式组织，可直接获取关联长度指数，确立了空间非均匀测量的可控途径。
中文摘要 AI 辅助
在受监测的量子电路中，测量诱导相变（MIPTs）通常通过在不同的均匀测量概率下制备稳态来表征。在此，我们通过在单个受监测的 Clifford 链中施加确定性测量梯度，引入了 MIPT 的空间实现。所得稳态包含共存的体积律、临界和面积律区域，点 $p(x)=p_c$ 作为空间临界切割。通过在这个分布上扫描纠缠可观测量，我们表明该相变由空间标度形式组织。虽然这种结构类似于时间驱动 MIPT 中的有限时间标度，但空间协议没有 Kibble-Zurek 动力学。相反，物理边界 $0\le p\le 1$ 施加了一个有限的线性窗口，产生了截止控制的渐近区域，其拟合指数提供了直接获取关联长度指数 $\nu$ 的途径。我们的结果将空间非均匀测量确立为在单个稳态中设计和探测测量诱导临界性的可控途径。
英文摘要
Measurement-induced phase transitions (MIPTs) in monitored quantum circuits are usually characterized by preparing steady states at different uniform measurement probabilities. Here we introduce a spatial realization of the MIPT by imposing a deterministic measurement gradient in a single monitored Clifford chain. The resulting steady state contains coexisting volume-law, critical, and area-law regions, with the point $p(x)=p_c$ acting as a spatial critical cut. By scanning entanglement observables across this profile, we show that the transition is organized by a spatial scaling form. Although this structure is analogous to finite-time scaling in temporally driven MIPT, the spatial protocol has no Kibble-Zurek dynamics. Instead, the physical bounds $0\le p\le 1$ impose a finite linear window, producing cutoff-controlled asymptotic regimes whose fitted exponents provide direct access to the correlation-length exponent $ν$. Our results establish spatially inhomogeneous measurements as a controlled route to engineer and probe measurement-induced criticality within a single steady state.
