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quantum information and quantum computation can process multiple tasks which are intractable with classical technologies .
quantum entanglement is no doubt a fundamental resource for a variety of quantum information processing tasks , such as super - dense coding , quantum cryptography and quantum error correction [ 1 - 4 ] .
strongly entangled , multi - partite states of qubits and qutrits are a central resource of quantum information science . these are frequently used in constructing many protocols , such as teleportation [ 5 ] , key distribution and quantum computation [ 6 ] .
the phenomenon of sudden loss of entanglement also termed as entanglement sudden death " esd has been investigated by a number of authors for bipartite and multipartite systems [ 7 - 10 ] .
yu and eberly [ 11 , 12 ] showed that entanglement loss occurs in a finite time under the action of pure vacuum noise in a bipartite state of qubits .
they found that , even though it takes infinite time to complete decoherence locally , the global entanglement may be lost in finite time .
recently , researchers have focused on relativistic quantum information in the filed of quantum information science due to conceptual and experimental reasons . in the last few years , much attention had been given to the study of entanglement shared between inertial and non - inertial observers by discussing how the unruh or hawking effect will influence the degree of entanglement [ 1322 ] .
most of the investigations in non - inertial frames are focused on the study of the quantum information in bipartite qubit system with one subsystem as an accelerated . since , it is  not possible to completely isolate a quantum system from its environment .
therefore , one needs to investigate the behavior of entanglement in the presence of environmental effects .
a major problem of quantum communication is to faithfully transmit unknown quantum states through a noisy quantum channel .
when quantum information is sent through a channel , the carriers of the information interact with the channel and get entangled with its many degrees of freedom .
this gives rise to the phenomenon of decoherence on the state space of the information carriers .
implementation of decoherence in non - inertial frames have been investigated by different authors [ 23 , 24 ] .
peres - horodecki [ 25 , 26 ] have studied entanglement of qubit - qubit and qubit - qutrit states and established separability criterion . according to this criterion , the partial transpose of a separable density matrix must have non - negative eigenvalues , where the partial transpose is taken over the smaller subsystem for qubit - qutrit case . for nonseparable states ,
the sum of the absolute values of the negative eigenvalues of the partial transpose gives the degree of entanglement of a density matrix also termed as negativity .
ann et al .
[ 27 ] have studied a qubit - qutrit system where they have shown the existence of esd under the influence of dephasing noise .    in this paper
, we study the effect of decoherence on a qubit - qutrit system in non - inertial frames by considering different noise models , such as , amplitude damping , depolarizing and phase damping channels .
we consider different couplings of the system and the environment where the system is influenced by global , local , or multi - local noises modeled in a number of scenarios .
we show that entanglement degradation occurs for various coupling of the system and the environment .
it is shown that different environments degrade the entanglement of the hybrid system differently .
we consider a composite system of a qubit @xmath0 and a qutrit @xmath1 that is coupled to a noisy environment both collectively and individually .
local and multi - local couplings describe the situation when the qubit and qutrit are independently influenced by their individual noisy environments . whereas , the global decoherence corresponds to the situation when it is influenced by both collective and multilocal noises at the same time .
the term collective coupling means when both the qubit and qutrit are influenced by the same noise .
the state shared by the two parties is an entangled qubit - qutrit state of the form [ 28]@xmath2where the two modes of minkowski spacetime that correspond to alice and rob are @xmath3 and @xmath4 respectively .
we assume that alice remain stationary while rob moves with uniform acceleration .
it is important to mention here that the above state is obtained after taking the trace over unobserved region iv [ 28 ] .
the interaction between the system and its environment introduces the decoherence to the system , which is a process of the undesired correlation between the system and the environment .
the evolution of a state of a quantum system in a noisy environment can be described by the super - operator @xmath5 in the kraus operator representation as [ 29 ]    @xmath6    where the kraus operators @xmath7 satisfy the following completeness relation    @xmath8    we have constructed the kraus operators for the evolution of the composite system from the single qubit kraus operators ( see table1 ) and qutrit kraus operators as given in equations ( 5 - 8 ) by taking their tensor product over all @xmath9 combination of @xmath10 indices    @xmath11    where @xmath12 and @xmath13 correspond to the number of kraus operators for a single qubit and qutrit channel respectively .
the single qutrit kraus operators for the amplitude damping channel are given by [ 30 ]    @xmath14    and the single qutrit kraus operators for the phase damping channel are given as    @xmath15    the single qutrit kraus operators for the depolarizing channel are given by [ 31 ]    @xmath16    @xmath17    where @xmath18 is the identity matrix of order 3 .
@xmath19    in the above equations , @xmath20 represents the quantum noise parameter and @xmath21 .
the evolution of the initial density matrix of the composite system when it is influenced by local and multi - local environments is given in kraus operator form as @xmath22and the evolution of the system when it is influenced by global environment is given in kraus operator representation as @xmath23where @xmath24 @xmath25 are the kraus operators of the multilocal coupling of qubit and qutrit individually and @xmath26 are the kraus operators of the collective coupling of the hybrid system . using equations ( 5 - 10 ) along with the initial density matrix of as given in equation ( 1 ) and taking the partial transpose over the smaller subsystem ( qubit )
, we find the eigenvalues of the final density matrix .
let the decoherence parameters for local and global noise of the qubit and qutrit be @xmath27 , @xmath28 and @xmath20 respectively .
the entanglement for all mixed states @xmath29 of a qubit - qutrit system is well quantified by the negativity [ 32]@xmath30where @xmath31  represents the negative eigenvalues of the partial transpose of the density matrix @xmath29 with respect to the smaller subsystem .
the eigenvalues of the partial transpose matrix when only the qubit is influenced by the amplitude damping channel are given by @xmath32the only possible negative eigenvalue is the fourth one and the negativity is calculated using the relation given in equation ( 11 ) .
the eigenvalues of the partial transpose matrix when only qutrit is influenced by the amplitude damping channel are given by@xmath33the only possible negative eigenvalue is the second one .
the eigenvalues of the partial transpose matrix when both qubit and qutrit are influenced by the amplitude damping channel are given by @xmath34% \end{array}% \right ) \right.\end{aligned}\]]the only possible negative eigenvalue is the fifth one .
the eigenvalues of the partial transpose matrix when the system is influenced by the global noise of amplitude damping channel are given by @xmath35% \end{array}% \right ) \right.\end{aligned}\]]the only possible negative eigenvalue is the fifth one .
the eigenvalues of the partial transpose matrix when only the qubit is influenced by the depolarizing channel are given by@xmath36the only possible negative eigenvalue is the third one .
the eigenvalues of the partial transpose matrix when only qutrit is influenced by the depolarizing channel are given by@xmath37the only possible negative eigenvalue is the fourth one .
the eigenvalues of the partial transpose matrix when both the qubit and the qutrit are influenced by the depolarizing channel are given by@xmath38the only possible negative eigenvalue is the fifth one .
the eigenvalues of the partial transpose matrix when the system is influenced by the global noise of depolarizing channel are given by@xmath39the only possible negative eigenvalue is the first one .
the eigenvalues of the partial transpose matrix when only qubit is influenced by the phase damping channel are given by@xmath40the only possible negative eigenvalue is the third one .
the eigenvalues of the partial transpose matrix when only qutrit is influenced by the phase damping channel are given by@xmath41the only possible negative eigenvalue is the third one .
the eigenvalues of the partial transpose matrix when both qubit and qutrit are influenced by the phase damping channel are given by@xmath42the only possible negative eigenvalue is the third one .
the eigenvalues of the partial transpose matrix when the system is influenced by the global noise of phase damping channel are given by@xmath43the only possible negative eigenvalue is the third one .
the negativity is calculated using equation ( 5 ) for all the above cases and results are discussed in detail in the next section .
in this work , we investigate the effect of decoherence on a qubit - qutrit system in non - inertial frames . in figure 1 , we plot negativity as a function of rob s acceleration , @xmath44  for decoherence parameters @xmath45 for amplitude damping channel .
it is seen that maximal entanglement degradation occurs under global noise .
it is also seen that the entanglement is degraded heavily as we increase the value of rob s acceleration .
however , the entanglement loss is consistent for all the cases and no esd behaviour is seen for any acceleration . in figure 2
, we plot the negativity as a function of rob s acceleration , @xmath44  for @xmath46 ( multi - local noise ) and @xmath47 ( global noise ) for depolarizing channel .
it is seen that depolarizing channel heavily degrades the entanglement as compared to amplitude damping channel , particularly in case of global decoherence . in figure 3
, we plot the negativity as a function of rob s acceleration , @xmath44  for @xmath48 ( multi - local noise ) and @xmath49 ( global noise ) for phase damping channel .
a similar behaviour of amplitude damping and phase damping channels is seen towards entanglement degradation .    in figure 4 , we plot the negativity as a function of rob s acceleration , @xmath44  for @xmath50 for amplitude damping , depolarizing and phase damping channels .
it is shown that depolarizing channel influences the entanglement of the system more heavily as compared to the other two channels .
on the other hand , for higher values of decoherence parameters , the amplitude damping channel have more influence on the entanglement degradation as clear from figure 5 .
further more , it is also seen that no esd occurs for any acceleration of rob for the entire range of decoherence parameters .
we analyze the effect of decoherence on a qubit - qutrit system under the influence of decoherence in non - inertial frames .
we consider different noise models such as amplitude damping , depolarizing and phase damping channels with different couplings of the system and the environment . we show that the entanglement sudden death can be avoided in non - inertial frames .
however , degradation of entanglement is seen due to unruh effect .
it is seen that for lower values of decoherence parameters , the depolarizing channel heavily degrades the entanglement of the system as compared to the amplitude damping and phase damping channels .
however , for higher values of decoherence parameters , amplitude damping channel heavily degrades the entanglement of the system . in conclusion
, no esd occurs for any value of rob s acceleration .
figures captions**figure 1**. the negativity is plotted as a function of rob s acceleration , @xmath44  for @xmath46 ( multi - local noise ) and @xmath49 ( global noise ) for amplitude damping channel.*figure 2*. the negativity is plotted as a function of rob s acceleration , @xmath44  for @xmath46 ( multi - local noise ) and @xmath49 ( global noise ) for depolarizing channel.*figure 3*. the negativity is plotted as a function of rob s acceleration , @xmath44  for @xmath46 ( multi - local noise ) and @xmath49 ( global noise ) for phase damping channel.*figure 4*. the negativity is plotted as a function of rob s acceleration , @xmath44  for @xmath50 for amplitude damping , depolarizing and phase damping channels.*figure 5*. the negativity is plotted as a function of rob s acceleration , @xmath44  for @xmath51 for amplitude damping , depolarizing and phase damping channels.*table 1*. single qubit kraus operators for amplitude damping , depolarizing and phase damping channels where @xmath20 represents the decoherence parameter .
we study the effect of decoherence on a qubit - qutrit system under the influence of global , local and multilocal decoherence in non - inertial frames . 
 we show that the entanglement sudden death can be avoided in non - inertial frames in the presence of amplitude damping , depolarizing and phase damping channels . 
 however , degradation of entanglement is seen due to unruh effect . 
 it is shown that for lower level of decoherence , the depolarizing channel degrades the entanglement more heavily as compared to the amplitude damping and phase damping channels . 
 however , for higher values of decoherence parameters , amplitude damping channel heavily degrades the entanglement of the hybrid system . 
 further more , no esd is seen for any value of rob s acceleration .    
 keywords : quantum decoherence ; entanglement ; non - inertial frames .