Entanglement harvesting and curvature of entanglement: A modular operator approach

• URL: http://arxiv.org/abs/2508.12497v2
• Date: Thu, 16 Oct 2025 23:53:34 GMT
• Title: Entanglement harvesting and curvature of entanglement: A modular operator approach
• Authors: Rupak Chatterjee,
• Abstract summary: An operator-algebraic framework based on Tomita-Takesaki modular theory is used to study aspects of quantum entanglement.<n>The entanglement structure of quantum fields is studied through the protocol of entanglement harvesting.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\rho$ and its modular reflection $J\rho J$. 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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