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Secure system state estimation is an important issue in smart grid to assure the reliability and security. In this paper, the case of a single observation station and Gaussian noise communication channel with an eavesdropper is considered. The channel capacity requirement is studied from the information theoretic perspective. The smart grid is modeled as a linear dynamic system. Then, the channel capacity requirement is studied for the state estimation of general linear dynamic systems and then applied in the system state estimation in smart grid. Numerical simulations are used to evaluate the capacity requirement in typical configurations of smart grid.