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In general, the reduced density matrix has components ρi=±1,j=±1(xA,xB;yA,yB). However, under the implicit assumption that the spatial and internal degrees of freedom of each detector are initially not entangled, and that the back-reaction on the spatial degrees of freedom can be ignored (ΔPΩ), the entanglement in the reduced density matrix 4, will correspond to virtually all of the entanglement between the detectors.
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