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the study of quantum information in noninertial framework is not only helpful for understanding some key questions in quantum mechanics @xcite , but it also plays an important role in the study of entropy and the information paradox of black holes @xcite . recently , much attention has been focused on the topic of the quantum information in a relativistic setting @xcite and , in particular , on how the unruh effect changes the degree of quantum entanglement @xcite and fidelity of teleportation @xcite .
however , it should be pointed out that all investigations in noninertial frames are confined to the studies of the quantum information in _ an isolated system_. however , in a realistic quantum system , the _ interaction _ between the quantum system and the surrounding environment is inevitable , and then the dynamics of the system is non - unitary ( although the combined system plus environment evolves in a unitary fashion ) .
the decoherence @xcite , which appears when a system interacts with its environment in a irreversible way , can be viewed as the transfer of information from system into the environment .
it plays a fundamental role in the description of the quantum - to - classical transition @xcite and has been successfully applied in the cavity qed @xcite and ion trap experiments @xcite .    in this article
we investigate the quantum decoherence of dirac fields in a noninertial system . for the sake of brevity and without loss of generality ,
we consider only the amplitude damping channel @xcite , which is the most typical quantum noisy channel and can be modeled by the spontaneous decay of a two - level quantum state in an electromagnetic field @xcite .
we assume that two observers , alice and rob , share an entangled initial state at the same point in flat minkowski spacetime .
after that alice stays stationary while rob moves with uniform acceleration .
we let one ( or both ) of the observers moves ( or stays ) in the noisy environment and discuss whether or not the quantum decoherence and the loss of entanglement generated by unruh radiation will influence each other .
a key question to be answered is : does r the entanglement appears to be sudden death @xcite or does it only disappears as time tends to infinity ?
we assume that alice has a detector sensitive only to mode @xmath0 and rob has a detector sensitive only to mode @xmath1 , and they share the maximally entangled initial state @xmath2 at the same point in minkowski spacetime , where @xmath3 and @xmath4 indicate minkowski modes described by alice and rob , respectively .
we then let alice remain stationary while rob moves with uniform acceleration .
from the perspective of rob the minkowski vacuum is found to be a two - mode squeezed state @xcite @xmath5 where @xmath6 , @xmath7 is rob s acceleration , @xmath8 is frequency of the dirac particle , @xmath9 is the speed of light in vacuum , and @xmath10 and @xmath11 indicate rindler modes in region @xmath12 and @xmath13 ( see fig .
[ rindler ] ) , respectively .
the only excited state is given by latexmath:[\ ] ] it is interesting to note that the concurrence is also @xmath39 for @xmath64 .
( color online ) the concurrence as functions of the decay parameter @xmath65 and acceleration parameter @xmath48 [ @xmath41 ( black line ) ,  @xmath42 ( dotted line ) ,  @xmath43 ( dashed green line ) ,  @xmath44 ( dashed blue line ) ,  @xmath45 ( dashed orange line ) ] when both alice and rob s qubits under decoherence . ]
figure ( [ erp2 ] ) shows time evolution of quantum entanglement when the total two qubits system is coupled to the environment .
it shows that , compared with the case of only rob s qubit undergoing decoherence , the entanglement decreases more rapidly as the acceleration increases .
it is interesting to note that the sudden death of entanglement appears at a finite time even for @xmath41 , and a lager acceleration also leads to an earlier appearance of the sudden death as the parameter @xmath65 increases .    in particular , when the acceleration approaches infinity , the sudden death appears when @xmath66 , whereas it happens when @xmath67 when only rob s qubit undergoes decoherence .
thus , we come to the conclusion that the decoherence and loss of entanglement generated by the unruh effect will influence each other in noninertial frames .
in conclusion , we have found that , unlike the isolated case in which the entanglement of dirac fields survives even in the limit of infinite acceleration @xcite , the entanglement could tend to zero for finite acceleration in this system ; and a lager acceleration leads to an earlier disappearance of entanglement if either one or both subsystems experience a decoherence .
thus , the decoherence and loss of entanglement generated by the unruh effect will influence each other remarkably in noninertial frames .
it is also shown that the sudden death of entanglement will appear for any acceleration when both of the two qubits interact with the environment . however ,
if only rob s qubit undergoes decoherence , the sudden death only takes place when the acceleration parameter is greater than the  critical point " , @xmath53 $ ] .
our results can be applied to the case in which alice moves along a geodesic while rob hovers near the event horizon with an uniform acceleration and one or both of them are in an amplitude - damping environment .
this work was supported by the national natural science foundation of china under grant no 10875040 ; a key project of the national natural science foundation of china under grant no 10935013 ; the national basic research of china under grant no .
2010cb833004 , the hunan provincial natural science foundation of china under grant no .
08jj3010 , pcsirt under grant no .
irt0964 , and the construct program of the national key discipline .
quantum decoherence , which appears when a system interacts with its environment in an irreversible way , plays a fundamental role in the description of quantum - to - classical transitions and has been successfully applied in some important experiments . here 
 , we study the decoherence in noninertial frames for the first time . 
 it is shown that the decoherence and loss of the entanglement generated by the unruh effect will influence each other remarkably . 
 it is interesting to note that in the case of the total system under decoherence , the sudden death of entanglement may appear for any acceleration . 
 however , in the case of only rob s qubit underging decoherence sudden death may only occur when the acceleration parameter is greater than a  critical point . "