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Entropic methodology for entanglement measures

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  • Deng, Wei
  • Deng, Yong

Abstract

Quantifying Entanglement is the key ingredient for the upcoming quantum information technology. Entanglement is hard to grasp, however, which brings about incomplete, indirect ways in proposed measures. Here we show that entropy, as the preferred mathematical quantity to express uncertainty in information theory, can be used to directly detect the entanglement from an arbitrary quantum state. Entanglement is defined as the difference of entropy between the state of system and its corresponding separable state with the same local properties. Remarkably, this general framework is a universal measure of entanglement applies to pure, multipartite, and mixed state. Furthermore, we introduce the disentanglement to find the corresponding separable state for bipartite systems, and give its generalization, called partial disentanglement, for multipartite systems, which breaks the barrier that only concerns the overall entanglement of quantum system, and then concerns the entanglement of a subsystem in composite system and the entanglement between subsystems. Besides, we show that our general framework satisfies the requirements of a proper measures of entanglement.

Suggested Citation

  • Deng, Wei & Deng, Yong, 2018. "Entropic methodology for entanglement measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 693-697.
    • Handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:693-697
    DOI: 10.1016/j.physa.2018.07.044
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    References listed on IDEAS

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    1. Kang, Bingyi & Chhipi-Shrestha, Gyan & Deng, Yong & Hewage, Kasun & Sadiq, Rehan, 2018. "Stable strategies analysis based on the utility of Z-number in the evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 202-217.
    2. Yin, Likang & Deng, Yong, 2018. "Toward uncertainty of weighted networks: An entropy-based model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 176-186.
    3. Rong Zhang & Baabak Ashuri & Yong Deng, 2017. "A novel method for forecasting time series based on fuzzy logic and visibility graph," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(4), pages 759-783, December.
    4. Vlatko Vedral, 2008. "Quantifying entanglement in macroscopic systems," Nature, Nature, vol. 453(7198), pages 1004-1007, June.
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    Cited by:

    1. Wei, Bo & Deng, Yong, 2019. "A cluster-growing dimension of complex networks: From the view of node closeness centrality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 80-87.
    2. Xiaozhuan Gao & Yong Deng, 2019. "The generalization negation of probability distribution and its application in target recognition based on sensor fusion," International Journal of Distributed Sensor Networks, , vol. 15(5), pages 15501477198, May.
    3. Wen, Tao & Deng, Yong, 2020. "The vulnerability of communities in complex networks: An entropy approach," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    4. Yige Xue & Yong Deng, 2020. "Refined Expected Value Decision Rules under Orthopair Fuzzy Environment," Mathematics, MDPI, vol. 8(3), pages 1-14, March.

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