Quantum Snapshots Reveal a Compact Conformal Boundary Mode

• URL: http://arxiv.org/abs/2608.14327v1
• Date: Fri, 14 Aug 2026 14:19:42 GMT
• Title: Quantum Snapshots Reveal a Compact Conformal Boundary Mode
• Abstract summary: A projective measurement of a many-body state produces a microscopic snapshot, usually viewed as random classical data.<n>We show that partial occupation snapshots of the critical XX chain contain a universal angle with a precise conformal meaning.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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