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Strong Superadditive Deficit of Coherence and Quantum Correlations Distribution

  • 1Institute of Physics, Chinese Academy of Sciences, Beijing 100190

  • 2Institute of Modern Physics, Northwest University, Xi'an 710127

  • 3Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127

  • 4School of Mathematics and Physics, The University of Queensland, Brisbane 4072, Australia

Funds: Supported by the National Natural Science Foundation of China under Grant Nos 11775177, 11775178, 11647057 and 11705146, the Special Research Funds of Shaanxi Province Department of Education under Grant No 16JK1759, the Basic Research Plan of Natural Science in Shaanxi Province under Grant No 2018JQ1014, the Major Basic Research Program of Natural Science of Shaanxi Province under Grant No 2017ZDJC-32, the Key Innovative Research Team of Quantum Many-Body Theory and Quantum Control in Shaanxi Province under Grant No 2017KCT-12, the Northwest University Scientific Research Funds under Grant No 15NW26, the Double First-Class University Construction Project of Northwest University, and the Australian Research Council through Discovery Projects under Grant No DP190101529.
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  • Received Date: April 23, 2019
  • Published Date: July 31, 2019
    Abstract
  • The definitions of strong superadditive deficit for relative entropy coherence and monogamy deficit of measurement-dependent global quantum discord are proposed. The equivalence between them is proved, which provides a useful criterion for the validity of the strong superadditive inequality of relative entropy coherence. In addition, the strong superadditive deficit of relative entropy coherence is proved to be greater than or equal to zero under the condition that bipartite measurement-dependent global quantum discord (GQD) does not increase under the discarding of subsystems. Using the Monte Carlo method, it is shown that both the strong superadditive inequality of relative entropy coherence and the monogamy inequality of measurement-dependent GQD are established under general circumstances. The bipartite measurement-dependent GQD does not increase under the discarding of subsystems. The multipartite situation is also discussed in detail.
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