Protecting Nonlocality Of Multipartite States By Feed-forward Control

Like quantum entanglement,quantum nonlocality is also a very important resource in quantum information.In quantum communication,the multipartite entangled states are usually locally produced and distributed among different users in different places to construct the quantum channel.However,this distribution process is always disturbed by noises,then the nonlocality of the states will decay and even lost and can not be used to construct the quantum channel.In this paper,we use a feed-forward control scheme to protect the nonlocality of multipartite states,and we only consider amplitude damping(AD)channel.The essence of this scheme is to change the protected state into the state almost immune to the noise channel before passing the channel,and then to recover it after passing the channel at cost of part of the success probability of protection.We let the first qubit of Bell state and the first two qubits of GHZ state pass the AD channel respectively and at the same time we use this scheme to protect them.We use Bell inequality and a modified Bell inequality to characterize the nonlocality of protected Bell state and protected GHZ state respectively.Comparing with the case of no protection,we find this scheme have a very good protection effect for both Bell state and GHZ state,and the entanglement is easier to be protected than the nonlocality.As we all know,the entanglement is the necessary but not sufficient condition of the nonlocality,however,the relation between them have not been understood clearly,we find that the nonlocality and the entanglement is not corresponding one by one.