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Classification of the entangled states 2 × M × N

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Abstract

We extend the matrix decomposition method (MDM) in classifying the 2 × N × N truly entangled states to 2 × M × N system under the condition of stochastic local operations and classical communication. It is found that the MDM is quite practical and convenient in operation for the asymmetrical tripartite states, and an explicit example of the classification of 2 × 6 × 7 quantum system is presented.

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References

  1. Einstein A., Podolsky B., Rosen N.: Can quantum-mechanical description of physical reality be considered complete?. Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

  2. Bell J.S.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964)

    Google Scholar 

  3. Ekert A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Bennett C.H., Bessette F., Grassard G., Salvail L., Smolin J.: Experimental quantum cryptography. J. Cryptol. 5, 3 (1992)

    Article  MATH  Google Scholar 

  5. Bennett C.H., Wiesner S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Mattle K., Weinfurter H., Kwiat P.G., Zeilinger A.: Dense Coding in Experimental Quantum Communication. Phys. Rev. Lett. 76, 4656 (1996)

    Article  ADS  Google Scholar 

  7. Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  8. Horodecki R., Horodecki P., Horodecki M., Horodecki K.: Quantum entanglement. Rev. Mod. Phys 81, 865 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Dür W., Vidal G., Cirac J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  10. Chen L., Chen Y.-X., Mei Y.-X.: Classification of multipartite entanglement containing infinitely many kinds of states. Phys. Rev. A 74, 052331 (2006)

    Article  ADS  Google Scholar 

  11. Cheng S., Li J., Qiao C.-F.: Classification of the entangled states of 2 × N × N. J. Phys. A 43, 055303 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  12. Chen L., Chen Y.-X.: Range criterion and classification of true entanglement in a 2 × M × N system. Phys. Rev. A 73, 052310 (2006)

    Article  ADS  Google Scholar 

  13. Cornelio M.F., de Toledo Piza A.F.R.: Classification of tripartite entanglement with one qubit. Phys. Rev. A 73, 032314 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  14. Horn R.A., Johnson C.R.: Matrix Analysis. Cambridge University, Cambridge (1985)

    MATH  Google Scholar 

  15. Cheng, S., Li, J., Qiao, C.-F.: Classification of the entangled state of 2 × 5 × 5 pure systems. J. Grad. Sch. Chin. Acad. Sci. 3, 303 (2009) (in chinese).

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Physics, Graduate University of the Chinese Academy of Sciences, YuQuan Road 19A, Beijing, 100049, China

    Jun-Li Li & Cong-Feng Qiao

  2. Theoretical Physics Center for Science Facilities (TPCSF), CAS, YuQuan Road 19B, Beijing, 100049, China

    Cong-Feng Qiao

Authors
  1. Jun-Li Li
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  2. Cong-Feng Qiao
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Correspondence to Cong-Feng Qiao.

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Li, JL., Qiao, CF. Classification of the entangled states 2 × M × N . Quantum Inf Process 12, 251–268 (2013). https://doi.org/10.1007/s11128-012-0370-2

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  • DOI: https://doi.org/10.1007/s11128-012-0370-2

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