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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• Revised Aug 5, 2026 (v3)
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's statistical treatment of exchange symmetry avoids the unphysical negative local entropies that arise from naive ln(2) subtraction, yielding spatial profiles that remain positive throughout. 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 in many-body systems.

AI Summary

The paper asks whether spatially resolved entanglement can be inferred from ensembles of one-body guide wavefunctions in Time-Dependent Quantum Monte Carlo (TDQMC), without constructing the full many-body wavefunction. It treats these guide waves as a statistical mixture in Hilbert space and identifies their Gram matrix with a covariance operator. The abstract states that its spectrum coincides with the Schmidt spectrum, linking ensemble statistics to entanglement measures. The proposed diagnostic is a functional standard deviation of the wavefunction ensemble. It is reported to track von Neumann entanglement entropy both globally and spatially, with local profiles obtained by partitioning the Monte Carlo walkers. Tests use one-dimensional, two-electron helium-atom and hydrogen-like-molecule models in bosonic and fermionic settings. For opposite-spin electrons, the results are reported to agree closely with strict conditional-wave calculations. For same-spin fermions, the TDQMC treatment of exchange produces nonnegative spatial profiles, avoiding the negative local entropies obtained by naively subtracting $\ln 2$ to remove an exchange contribution. Only the abstract is available, so the assumptions behind the spectral identification, the precise local-entropy construction, numerical errors, and computational scaling cannot be assessed here. The stated demonstrations are limited to one-dimensional two-electron models; the abstract provides no quantitative accuracy figures or tests in larger systems.

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DOI
10.1021/acsomega.6c05016
Comments
published in ACS Omega, 2026

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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's statistical treatment of exchange symmetry avoids the unphysical negative local entropies that arise from naive ln(2) subtraction, yielding spatial profiles that remain positive throughout. 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 in many-body systems.
The paper asks whether spatially resolved entanglement can be inferred from ensembles of one-body guide wavefunctions in Time-Dependent Quantum Monte Carlo (TDQMC), without constructing the full many-body wavefunction. It treats these guide waves as a statistical mixture in Hilbert space and identifies their Gram matrix with a covariance operator. The abstract states that its spectrum coincides with the Schmidt spectrum, linking ensemble statistics to entanglement measures.
The proposed diagnostic is a functional standard deviation of the wavefunction ensemble. It is reported to track von Neumann entanglement entropy both globally and spatially, with local profiles obtained by partitioning the Monte Carlo walkers. Tests use one-dimensional, two-electron helium-atom and hydrogen-like-molecule models in bosonic and fermionic settings. For opposite-spin electrons, the results are reported to agree closely with strict conditional-wave calculations. For same-spin fermions, the TDQMC treatment of exchange produces nonnegative spatial profiles, avoiding the negative local entropies obtained by naively subtracting ln⁡2\ln 2ln2 to remove an exchange contribution.
Only the abstract is available, so the assumptions behind the spectral identification, the precise local-entropy construction, numerical errors, and computational scaling cannot be assessed here. The stated demonstrations are limited to one-dimensional two-electron models; the abstract provides no quantitative accuracy figures or tests in larger systems.
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Abstract By using stochastic ensembles of walkers in physical and in one-body Hilbert spaces the recently proposed time-dependent quantum Monte Carlo (TDQMC) method offers the unique capability to calculate one-body density matrices at fully correlated level, without referencing the many-body quantum state. Here TDQMC is applied to study entanglement of simple systems such as Moshinsky atom (oscillator potentials) and atoms with Coulomb potentials in one spatial dimension. Our findings indicate that the dynamic entanglement of atoms exposed to powerful ultrashort laser pulse can be easily manipulated by introducing an appropriate phase modulation where the negative chirp enhances the entanglement while the positive one suppresses it. These findings can be used to explore the correlation properties of different constituents of complex quantum systems subjected to appropriately shaped laser radiation.
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We investigate disordered one- and two-dimensional Heisenberg spin lattices across the transition from integrability to quantum chaos from both statistical many-body and quantum-information perspectives. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implication of the basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of relative delocalization is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and generalized entanglement are investigated in a wide parameter regime by using a family of spin- and fermion-purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive correlation between entanglement, delocalization, and integrability is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.