International Journal of Theoretical Physics

, Volume 58, Issue 4, pp 1269–1281 | Cite as

Constructing Entanglement Witnesses for Infinite-Dimensional Systems

  • Jinchuan HouEmail author
  • Wenli Wang


We generalize the results in Yu and Liu (Phys. Rev. Lett. 95, 150504, 2005) and Hou and Guo (Int. J. Theor. Phys. 50, 1245–1254, 2011) to infinite-dimensional systems and answer a problem raised in the second paper. Consider a bipartite system HK with dimH = dimK = . We show that (1) for any orthonormal sequences\(\{E_{k}\}_{k = 1}^{\infty }\) and\(\{F_{k}\}_{k = 1}^{\infty }\) consist of observables respectively in\(\mathcal {C}_{2}(H)\) and\(\mathcal {C}_{2}(K)\), if\({\sum }_{k} E_{k} \otimes F_{k}\) converges under the weak operator topology and if\(W=I-{\sum }_{k} E_{k}\otimes F_{k}\) is not positive, then W is a decomposable entanglement witness; (2) every state ρ of system HK has a Schmidt decomposition\(\rho = {\sum }_{k} \delta _{k} E_{k} \otimes F_{k}\) with {Ek} and {Fk} orthonormal sequences of observables.


Infinite-dimensional systems Entanglement states PPT states Entanglement witnesses 



This work is partially supported by National Natural Science Foundation of China (11671294).


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Authors and Affiliations

  1. 1.Department of MathematicsTaiyuan University of TechnologyTaiyuanPeople’s Republic of China

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