Einstein-Podolsky-Rosen Entanglement and Quantum Nonlocality for an Electron in a Uniform Magnetic Field

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 p_x and p_y 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.