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We theoretically investigate the joint photodetection probabilities of thebiexciton-exciton cascade in single semiconductor quantum dots and analyticallyderive the density matrix and the Bell's inequalities of the entangled state.Our model includes different mechanisms that may spoil or even destroyentanglement such as dephasing, energy splitting of the relay excitonic statesand incoherent population exchange between these relay levels. We explicitlyrelate the fidelity of entanglement to the dynamics of these processes andderive a threshold for violation of Bell's inequalities. Applied to standardInAs/GaAs self-assembled quantum dots, our model indicates that spontaneousemission enhancement of the excitonic states by cavity effects increases thefidelity of entanglement to a value allowing for violation of Bell'sinequalities.

Bell inequalities and density matrix for polarization entangled photons out of a two-photon cascade in a single quantum dot