Bell-state correlation in electric currents through lead electrodes connected to a quantum dot

We study quantum entanglement that is excited in currents through lead electrodes connected to a quantum dot. To assess the emerging entanglement among the lead electrode, we use Bell’s inequality with cross-correlations of current fluctuations [1]. The correlations of the current fluctuations are calculated by using the Anderson impurity model and Green's function in the Keldysh formalism. Electron-hole pairs are induced between two electric leads.
We show that quantum entanglement can be formed in the current even if there is no effective Coulomb interactions in the quantum dot. Namely, we investigate current that is induced by sequential tunneling or free quasiparticles scattering in the Kondo regime.
Specifically, we find that application of bias-voltages among the lead electrode generate electron-hole, electron-electron, and hole-hole pairs are excited among the lead electrodes. Thsese pairs can violate Bell's inequality
[1] N. M. Chtchelkatchev, G. Blatter, G. B. Lesovik, and T. Martin, Phys. Rev. B 66, 161320(R) (2002).