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Time evolution of an entangled initial state in coupled quantum dots with Coulomb correlations

We analyzed the dynamics of the initial singlet electronic state in the two interacting single-level quantum dots (QDs) with Coulomb correlations, weakly tunnel coupled to an electronic reservoir. We obtained correlation functions of all orders for the electrons in the QDs by decoupling high-order correlations between localized and band electrons in the reservoir. We proved that for arbitrary mixed state the concurrence and entanglement can be determined from the average value of particular combinations of electron's pair correlation functions. Analysis of the pair correlation functions time evolution allows to follow the changes of concurrence and entanglement during the relaxation processes. We investigated the dependence of concurrence on the value of Coulomb interaction and the energy levels spacing and found it's non-monotonic behavior in the non-resonant case. We also demonstrated that the behavior of pair correlation functions for two-electron entangled state in coupled QDs points to the fulfillment of the Hund's rule for the strong Coulomb interaction. We revealed the appearance of dynamical inverse occupation of the QDs energy levels during the relaxation processes. Our results open up further perspectives in solid state quantum information based on the controllable dynamics of the entangled electronic states.