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arXiv:2605.01728 · ACS Omega

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

Ivan P. Christov

quant-phSubmitted May 3, 2026• Announced May 5, 2026• 0 citations
v1 · May 3, 2026v2 · Jul 30, 2026v3 · Aug 5, 2026
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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.

DOI
10.1021/acsomega.6c05016

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