International Journal of Theoretical Physics

, Volume 57, Issue 9, pp 2722–2737 | Cite as

Quantum Non-Markovianity via the Covariance Matrix

  • Yajing FanEmail author
  • Liang Chen
  • Huaixin Cao
  • Huixian Meng


In this paper, we propose a new characterization of non-Markovian quantum evolution based on the covariance matrix. The fundamental properties of covariance matrices are elucidated. The measure captures quite directly the characteristics of non-Markovianity from the perspective of uncertainty. We consider several typical examples and compare the covariance matrix characterization of quantum non-Markovianity with Fisher-information matrix, divisibility and the Breuer-Laine-Piilo characterization of quantum non-Markovianity.


Markovianity Covariance matrix Quantum evolution 



This subject was supported by the NNSF of China (Nos. 11701011, 11601300, 61462002, 11761001, 11761003, 61463001), the SRP for North Minzu University (No. 2017SXKY02),the First-Class Disciplines Foundation of Ningxia(No. NXYLXK20 17B09).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceNorth Minzu UniversityYinchuanChina
  2. 2.Department of MathematicsChangji CollegeChangjiChina
  3. 3.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina
  4. 4.Theoretical Physics Division, Chern Institute of MathematicsNankai UniversityTianjinChina

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