Statistics of Marginal Wavefunctions as a Real-Space Diagnostic of Quantum Entanglement

• URL: http://arxiv.org/abs/2605.01728v1
• Date: Sun, 03 May 2026 05:56:08 GMT
• Title: Statistics of Marginal Wavefunctions as a Real-Space Diagnostic of Quantum Entanglement
• Abstract summary: We show that the Gram matrix acts as a covariance operator whose spectrum coincides with the Schmidt spectrum.<n>The associated functional standard deviation closely tracks the von Neumann entanglement entropy both globally and locally.<n>For same-spin fermions, TDQMC statistical treatment of exchange symmetry yields positive, physically consistent local entropies.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a statistical framework for extracting spatially resolved entanglement directly from an ensemble of marginal (one-body) wavefunctions in Time-Dependent Quantum Monte Carlo (TDQMC). Treating the guide waves as a statistical mixture in Hilbert space, we show that the Gram matrix acts as a covariance operator whose spectrum coincides with the Schmidt spectrum. The associated functional standard deviation closely tracks the von Neumann entanglement entropy both globally and locally via walker partitioning, providing a physically transparent real-space diagnostic of quantum correlations without requiring construction of the full many-body wavefunction. Applications to one-dimensional two-electron bosonic and fermionic systems (helium atom and hydrogen-like molecule) demonstrate excellent agreement with strict conditional-wave results for opposite-spin electrons. For same-spin fermions, TDQMC statistical treatment of exchange symmetry yields positive, physically consistent local entropies. The method establishes a direct bridge between classical ensemble statistics and quantum entanglement measures, offering a computationally efficient real-space diagnostic tool for mapping the spatial distribution of correlations.

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