量子快照揭示紧致共形边界模式
Quantum Snapshots Reveal a Compact Conformal Boundary Mode
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中文总结 AI 辅助
该研究发现临界XX链的量子快照含普适共形角度，通过测量位点定义紧致变量δ_L，其标度极限符合高斯分布，为共形边界条件的玻恩平均零模提供微观基础。
中文摘要 AI 辅助
对多体态的投影测量会产生微观快照，通常被视为随机经典数据。我们证明临界XX链的部分占据快照包含一个具有精确共形意义的普适角度。将环划分为两个已测量弧和两个未测量弧，我们为观测到的占据赋予与几何相关的共形边权重，得到一个紧致变量δ_L。在每个有限尺寸下，δ_L仅由已测量位点确定；证明中使用的特定完整构型提升量X_L还依赖于未观测粒子。该角度是精确的微观紧致坐标，其标度极限规律为相关共形四边形的相对狄利克雷相位——即连续测量后描述中与电荷共轭的边界坐标。精确自由费米子行列式可给出其所有傅里叶矩。我们证明该提升量变为高斯分布，方差为2h(ζ)，其中h(ζ)为矩形模，因此⟨e^(iqδ_L)⟩→e^(-h(ζ)q²)。由此，原始量子快照实现了圆上的热核，并为波动共形边界条件下玻恩平均的紧致零模部分提供了结果层面的微观基础。
英文摘要
A projective measurement of a many-body state produces a microscopic snapshot, usually viewed as random classical data. We show that partial occupation snapshots of the critical XX chain contain a universal angle with a precise conformal meaning. Dividing the ring into two measured and two unmeasured arcs, we assign geometry-dependent conformal side weights to the observed occupations and obtain a compact variable $δ_L$. At every finite size, $δ_L$ is fixed by the measured sites alone; the particular complete-configuration lift $X_L$ used in the proof additionally depends on unobserved particles. This angle is an exact microscopic compact coordinate whose scaling-limit law is that of the relative Dirichlet phase of the associated conformal quadrilateral---the boundary coordinate conjugate to charge in continuum post-measurement descriptions. Exact free-fermion determinants yield all of its Fourier moments. We prove that the lift becomes Gaussian with variance $2h(ζ)$, where $h(ζ)$ is the rectangle modulus, and hence $\langle e^{\ii qδ_L}\rangle\to e^{-h(ζ)q^2}$. Thus raw quantum snapshots realize the heat kernel on a circle and provide an outcome-level microscopic foundation for the compact zero-mode sector of Born averages over fluctuating conformal boundary conditions.
