Photons and electrons are the key quantum media for the quantum information processing based on solid state devices. Here we consider the key elements to realize the quantum repeater and reveal the underlying physics of relevant elementary processes. Especially, we discuss the quantum state transfer between a single photon and a single electron and analyze the performance of the operation, clarifying the conditions to achieve the high fidelity of the quantum state transfer. We also investigate quantum dynamics in the electron-nuclei coupled spin system in quantum dots and predict a couple of new phenomena related to the correlations induced by the hyperfine interaction, namely bunching and revival in the electron spin measurements. The underlying mechanism is the squeezing and increase in the purity of the nuclear spin state through the electron spin measurements. These findings will open the way to the long-lived quantum memory based on nuclear spins.
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