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Lower bounds of concurrence for N-qubit systems and the detection of k-nonseparability of multipartite quantum systems

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Abstract

Concurrence, as one of the entanglement measures, is a useful tool to characterize quantum entanglement in various quantum systems. However, the computation of the concurrence involves difficult optimizations and only for the case of two qubits, an exact formula was found. We investigate the concurrence of four-qubit quantum states and derive analytical lower bound of concurrence using the multiqubit monogamy inequality. It is shown that this lower bound is able to improve the existing bounds. This approach can be generalized to arbitrary qubit systems. We present an exact formula of concurrence for some mixed quantum states. For even-qubit states, we derive an improved lower bound of concurrence using a monogamy equality for qubit systems. At the same time, we show that a multipartite state is k-nonseparable if the multipartite concurrence is larger than a constant related to the value of k, the qudit number and the dimension of the subsystems. Our results can be applied to detect the multipartite k-nonseparable states.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos: 11371005, 11475054, Hebei Natural Science Foundation of China under Grant Nos: A2014205060, A2016205145.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, China

    Xianfei Qi & Ting Gao

  2. College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang, 050024, China

    Fengli Yan

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  1. Xianfei Qi
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  2. Ting Gao
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  3. Fengli Yan
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Correspondence to Ting Gao.

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Qi, X., Gao, T. & Yan, F. Lower bounds of concurrence for N-qubit systems and the detection of k-nonseparability of multipartite quantum systems. Quantum Inf Process 16, 23 (2017). https://doi.org/10.1007/s11128-016-1450-5

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