Related papers: Tomita-Takesaki theory and quantum concurrence

Tomita-Takesaki theory and quantum concurrence

URL: http://arxiv.org/abs/2406.15900v1
Date: Sat, 22 Jun 2024 17:35:02 GMT
Title: Tomita-Takesaki theory and quantum concurrence
Authors: Rupak Chatterjee,
Abstract summary: The quantum entanglement measure of concurrence is shown to be directly calculable from a Tomita- Takesaki modular operator framework constructed from the local von Neumann algebras of observables for two quantum systems.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The quantum entanglement measure of concurrence is shown to be directly calculable from a Tomita- Takesaki modular operator framework constructed from the local von Neumann algebras of observables for two quantum systems. Specifically, the Tomita-Takesaki modular conjugation operator $J$ that links two separate systems with respect to their von Neumann algebras is related to the quantum concurrence $C$ of a pure bi-variate entangled state composed from these systems. This concurrence relation provides a direct physical meaning to $J$ as both a symmetry operator and a quantitative measure of entanglement. This procedure is then demonstrated for a supersymmetric quantum mechanical system and a real scalar field interacting with two entangled spin-$\frac{1}{2}$ Unruh-DeWitt qubit detectors. For the latter system, the concurrence result is shown to be consistent with some known results on the Bell-CHSH inequality for such a system.

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