The entangled behavior of different dimensional systems driven by classical external random field is investigated. The amount of the survival entanglement between the components of each system is quantified. There are different behaviors of entanglem
ent that come into view decay, sudden death, sudden birth and long-lived entanglement. The maximum entangled states which can be generated from any of theses suggested systems are much fragile than the partially entangled ones. The systems of larger dimensions are more robust than those of smaller dimensions systems, where the entanglement decay smoothly, gradually and may vanish for a very short time. For the class of $2times 3$ dimensional system, the one parameter family is found to be more robust than the two parameters family. Although the entanglement of driven $ 2 times 3$ dimensional system is very sensitive to the classical external random field, one can use them to generate a long-lived entanglement.
A general form of a two-qubit system is obtained under the effect of Lorentz transformation. We investigate extensively some important classes in the context of quantum information. It is shown Lorentz transformation causes a decay of entanglement an
d consequently information loses. On the other hand, it generates entangled states between systems prepared initially in a separable states. The partial entangled states are more robust under Lorentz transformation than maximally entangled states. Therefore the rate of information lose is larger for maximum entangled states compared with that for partially entangled states.
The speed of quantum computation is investigated through the time evolution of the speed of the orthogonality. The external field components for classical treatment beside the detuning and the coupling parameters for quantum treatment play important
roles on the computational speed. It has been shown that the number of photons has no significant effect on the speed of computation. However, it is very sensitive to the variation in both detuning and the interaction coupling parameters.
