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We show that there exists the precise Einstein-Podolsky-Rosen entanglement for an electron in a uniform magnetic field. Specifically, the x- and y-coordinates of the electron as well as the corresponding canonical momenta px and pv become sharply correlated, which is a novel fact unnoticed before. When a harmonic potential is added to the system, the original vacuum state of the system becomes a squeezed vacuum state, whose quantum nonlocality is then demonstrated.