  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.
