Conditions for separability in multiqubit systems with an accelerating qubit using a conditional entropy

Abstract

We study the separability in multiqubit pure and mixed Greenberger-Horne-Zeilinger (GHZ) and W states with an accelerating qubit using the Abe-Rajagopal (AR) $ q $-conditional entropy. We observe that the pure multiqubit GHZ and W states in the inertial : non-inertial bipartition with one of their qubits accelerated will remain non-separable irrespective of the qubit's acceleration. In these systems, we captured the variation of their non-separability with respect to the acceleration of the qubit and the AR $ q $-conditional entropy parameter $ q $. However, in the corresponding multiqubit mixed states obtained by introducing a global noise to the above pure states, one could get stronger conditions on their separability in the inertial : non-inertial bipartition, in terms of the acceleration of the qubit, noise parameter, and the number of qubits in the system, in the asymptotic limit of parameter $ q $. These conditions obtained from the AR $ q $-conditional entropy serve as necessary conditions for separability in such multiqubit states with a relativistic qubit.