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  • Open Access

Entanglement harvesting and curvature of entanglement: A modular operator approach

Rupak Chatterjee*

  • Department of Applied Physics, New York University, 2 MetroTech Center, Brooklyn, New York 11201, USA

  • *Contact author: Rupak.Chatterjee@nyu.edu
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Phys. Rev. D 112, 085025 – Published 28 October, 2025

DOI: https://doi.org/10.1103/jjjg-6pht

Abstract

An operator-algebraic framework based on Tomita-Takesaki modular theory is used to study aspects of quantum entanglement via the application of the modular conjugation operator J. The entanglement structure of quantum fields is studied through the protocol of entanglement harvesting whereby quantum correlations evolve through the time evolution of qubit detectors coupled to a Bosonic field. Modular conjugation operators are constructed for Unruh-Dewitt type qubits interacting with a scalar field such that initially unentangled qubits become entangled. The entanglement harvested in this process is directly quantified by an expectation value involving J offering a physical application of this operator. The modular operator formalism is then extended to the Markovian open system dynamics of coupled qubits by expressing entanglement monotones as functionals of a state ρ and its modular reflection JρJ. The second derivative of such functionals with respect to an external coupling parameter, termed the curvature of entanglement, provides a natural measure of entanglement sensitivity. At points of modular self-duality, the curvature of entanglement coincides with the quantum Fisher information measure. These results demonstrate that the modular conjugation operator J captures both the harvesting of entanglement from quantum fields and the curvature of entanglement in coupled qubit dynamics providing parallel modular structures that connect these systems.

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Phys. Rev. D 112, 085025– Published 28 October, 2025
  • Received 23 August 2025
  • Accepted 16 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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