The classical and quantum correlations sharing between modes of the Dirac fields in the noninertial frame are investigated. It is shown that: (i) The classical correlation for the Dirac fields decreases as the acceleration increases, which is different from the result of the scalar field that the classical correlation is independent of the acceleration; (ii) There is no simple dominating relation between the quantum correlation and entanglement for the Dirac fields, which is unlike the scalar case where the quantum correlation is always over and above the entanglement; (iii) As the acceleration increases, the correlations between modes I and II and between modes A and II increase, but the correlations between modes A and I decrease.

How the Hawking effect and the prepared states influence the entanglement distillability of Dirac fields in the Schwarzschild spacetime is studied by using the Werner states which are composed of the maximum or generic entangled states. It is found that the states are entangled when the parameter of the Werner states, F, satisfies τ < F ≤ 1 in which τ is influenced both by the Hawking temperature of the black hole and energy of the fields. It is also shown that although the parameter of the generic entangled states, α, affects the entanglement, it does not change the range of the parameter, F, where the states are entangled for the case of generic entangled states.

Under amplitude damping channel, the dependence of the entanglement on the initial states and , which reduce to four orthogonal Bell states if we take the parameter of statesare investigated. We find that the entanglements for different initial states will decay along different curves even with the same acceleration and parameter of the states. We note that, in an inertial frame, the sudden death of the entanglement for will occur if, while it will not take place for for any α. We also show that the possible range of the sudden death of the entanglement for is larger than that forThere exist two groups of Bell state here we can't distinguish only by concurrence.

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