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-noninertial bipartition with one of their qubits accelerated will remain nonseparable irrespective of the qubit's acceleration. In these systems, we capture the variation of their nonseparability 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, we could get stronger conditions on their separability in the inertial-noninertial bipartition, in terms of the acceleration of the qubit, the noise parameter, and the number of qubits in the system, in the asymptotic limit of the 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.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-noninertial bipartition with one of their qubits accelerated will remain nonseparable irrespective of the qubit's acceleration. In these systems, we capture the variation of their nonseparability 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, we could get stronger conditions on their separability in the inertial-noninertial bipartition, in terms of the acceleration of the qubit, the noise parameter, and the number of qubits in the system, in the asymptotic limit of the 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.

arXiv:2404.02716Physical Review ASep 4, 202414 citations

Classification of multiqubit mixed states: Separability and distillability properties

Wolfgang Dür, J. I. Cirac

We give a complete, hierarchic classification for arbitrary multiqubit mixed states based on the separability properties of certain partitions. We introduce a family of N-qubit states to which any arbitrary state can be depolarized. This family can be viewed as the generalization of Werner states to multiqubit systems. We fully classify those states with respect to their separability and distillability properties. This provides sufficient conditions for nonseparability and distillability for arbitrary states.We give a complete, hierarchic classification for arbitrary multiqubit mixed states based on the separability properties of certain partitions. We introduce a family of N-qubit states to which any arbitrary state can be depolarized. This family can be viewed as the generalization of Werner states to multiqubit systems. We fully classify those states with respect to their separability and distillability properties. This provides sufficient conditions for nonseparability and distillability for arbitrary states.

arXiv:quant-ph/9911044Physical Review AMar 17, 2000291 citations

Beyond the Entanglement of Qubit Pairs in Multipartite Systems

S. Shelly Sharma, Naresh Kumar Sharma

Jan 1, 20221 citation

Comparability of multipartite entanglement

Zhengfeng Ji, Runyao Duan, Mingsheng Ying

arXiv:quant-ph/0407001Physics Letters AAug 31, 20046 citations

Computation of the geometric measure of entanglement for pure multiqubit states

Lin Chen, Aimin Xu, Huangjun Zhu

We provide methods for computing the geometric measure of entanglement for two families of pure states with both experimental and theoretical interests: symmetric multiqubit states with non-negative amplitudes in the Dicke basis and symmetric three-qubit states. In addition, we study the geometric measure of pure three-qubit states systematically in virtue of a canonical form of their two-qubit reduced states and derive analytical formulas for a three-parameter family of three-qubit states. Based on this result, we further show that the W state is the maximally entangled three-qubit state with respect to the geometric measure.We provide methods for computing the geometric measure of entanglement for two families of pure states with both experimental and theoretical interests: symmetric multiqubit states with non-negative amplitudes in the Dicke basis and symmetric three-qubit states. In addition, we study the geometric measure of pure three-qubit states systematically in virtue of a canonical form of their two-qubit reduced states and derive analytical formulas for a three-parameter family of three-qubit states. Based on this result, we further show that the W state is the maximally entangled three-qubit state with respect to the geometric measure.

arXiv:0911.1493Physical Review ASep 3, 201059 citations

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-noninertial bipartition with one of their qubits accelerated will remain nonseparable irrespective of the qubit's acceleration. In these systems, we capture the variation of their nonseparability 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, we could get stronger conditions on their separability in the inertial-noninertial bipartition, in terms of the acceleration of the qubit, the noise parameter, and the number of qubits in the system, in the asymptotic limit of the 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.