Entanglement Density Gradient Mapping (EDGM): A Field-Theoretic Approach to Spatial Variations of Quantum Entanglement

Jincheng Zhang

Published Aug 17, 2026• 0 citations

Abstract

The quantification of quantum entanglement has traditionally relied on scalar measures such as the von Neumann entropy, which captures the total amount of entanglement between two subsystems of a bipartite system. However, these scalar measures neglect spatial structure and do not account for how entanglement distributes or varies across a quantum medium. In this work we introduce the concept of an entanglement density gradient mapping (EDGM), which defines a spatial gradient of the entanglement entropy, denoted ∇S_E, and interprets it as a continuous entanglement field. We develop a formalism that extends the standard entanglement entropy to a spatially resolved density, S_E(x), and derive the governing equations for the entanglement field in terms of local Hamiltonian dynamics and correlation functions. By treating ∇S_E as a vector field, we uncover a natural geometric structure underlying quantum correlations, paving the way for the construction of a quantum information geometry. The EDGM framework predicts new phenomena, such as entanglement currents and vortices, that could be observed in large-scale quantum simulators. We discuss potential experimental implementations using ultracold atoms in optical lattices and trapped ion chains, and outline how EDGM could guide the design of quantum devices with spatially engineered entanglement profiles. The proposed mapping not only enriches our understanding of entanglement distribution but also offers a new language for describing quantum many-body systems, with implications for quantum computation, communication, and fundamental physics.

DOI: 10.5281/zenodo.21972642

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