How the Hawking effect and prepared states affect Entanglement distillability of Dirac fields

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 $\tau<F\leq 1$ in which $\tau$ 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, $\alpha$, 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.