Generalized Choi states and 2-distillability of quantum states

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Abstract

We investigate the distillability of bipartite quantum states in terms of positive and completely positive maps. We construct the so-called generalized Choi states and show that it is distillable when it has negative partial transpose. We convert the distillability problem of 2-copy \(n\times n\) Werner states into the determination of the positivity of an Hermitian matrix. We obtain several sufficient conditions by which the positivity holds. Further, we investigate the case \(n=3\) by the classification of \(2\times 3\times 3\) pure states.

Keywords

Positive linear maps Completely positive linear maps Completely copositive linear maps Distillability problem Generalized Choi states 2-Copy \(n\times n\) Werner 

Notes

Acknowledgements

Lin Chen was supported by Beijing Natural Science Foundation (4173076), the NNSF of China (Grant No. 11501024), and the Fundamental Research Funds for the Central Universities (Grant Nos. KG12001101, ZG216S1760 and ZG226S17J6). Wai-Shing Tang was partially supported by Singapore Ministry of Education Academic Research Fund Tier 1 Grant (No. R-146-000-193-112). Yu Yang was supported by Chongqing Technology and Business University Research Fund.

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Authors and Affiliations

  1. 1.School of Mathematics and Systems ScienceBeihang UniversityBeijingChina
  2. 2.International Research Institute for Multidisciplinary ScienceBeihang UniversityBeijingChina
  3. 3.Department of MathematicsNational University of SingaporeSingaporeRepublic of Singapore
  4. 4.Department of Mathematics and StatisticsChongqing Technology and Business UniversityChongqingChina

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