The Gram matrix of marginal wavefunctions in TDQMC acts as a covariance operator whose spectrum matches the Schmidt spectrum, so its functional standard deviation tracks von Neumann entanglement entropy both globally and locally.
The effective rank: A measure of effective dimensionality
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Statistics of Marginal Wavefunctions as a Real-Space Diagnostic of Quantum Entanglement
The Gram matrix of marginal wavefunctions in TDQMC acts as a covariance operator whose spectrum matches the Schmidt spectrum, so its functional standard deviation tracks von Neumann entanglement entropy both globally and locally.