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Uncertainty Relation and Inseparability Criterion

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Abstract

We investigate the Peres–Horodecki positive partial transpose criterion in the context of conserved quantities and derive a condition of inseparability for a composite bipartite system depending only on the dimensions of its subsystems, which leads to a bi-linear entanglement witness for the two qubit system. A separability inequality using generalized Schrodinger–Robertson uncertainty relation taking suitable operators, has been derived, which proves to be stronger than the bi-linear entanglement witness operator. In the case of mixed density matrices, it identically distinguishes the separable and non separable Werner states.

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References

  1. Schrödinger, E.: Die gegenwrtige situation in der quantenmechanik. Die Naturwissenschaften 23, 807 (1935)

    Article  ADS  MATH  Google Scholar 

  2. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777 (1935)

    Article  ADS  MATH  Google Scholar 

  3. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70(13), 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Bennett, C.H., Wiesner, S.J.: Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69(20), 2881 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  6. Ekert, A.K.: Quantum cryptography based on bells theorem. Phys. Rev. Lett. 67(6), 661 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Raussendorf, R., Browne, D.E., Briegel, H.J.: Measurement-based quantum computation on cluster states. Phys. Rev. A 68(2), 022312 (2003)

    Article  ADS  Google Scholar 

  8. Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77(8), 1413 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sucient conditions. Phys. Lett. A 223(1), 18 (1996)

    MathSciNet  MATH  Google Scholar 

  10. Simon, R.: Peres-horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 84(12), 2726 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  11. Duan, L.-M., Giedke, G., Cirac, J.I., Zoller, P.: Inseparability criterion for continuous variable systems. Phys. Rev. Lett. 84(12), 2722 (2000)

    Article  ADS  MATH  Google Scholar 

  12. Agarwal, C.S., Biswas, A.: Inseparability inequalities for higher order moments for bipartite systems. New J. Phys. 7(1), 211 (2005)

    Article  ADS  Google Scholar 

  13. Robertson, H.P.: An indeterminacy relation for several observables and its classical interpretation. Phys. Rev. 46(9), 794 (1934)

    Article  ADS  MATH  Google Scholar 

  14. Nha, H.: Entanglement condition via su (2) and su (1, 1) algebra using schrödinger-robertson uncertainty relation. Phys. Rev. A 76(1), 014305 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  15. Gühne, O.: Characterizing entanglement via uncertainty relations. Phys. Rev. Lett. 92(11), 117903 (2004)

    Article  ADS  Google Scholar 

  16. Gillet, J., Bastin, T., Agarwal, G.S.: Multipartite entanglement criterion from uncertainty relations. Phys. Rev. A 78(5), 052317 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  17. Nha, H., Zubairy, M.S.: Uncertainty inequalities as entanglement criteria for negative partial-transpose states. Phys. Rev. Lett. 101(13), 130402 (2008)

    Article  ADS  Google Scholar 

  18. Biswas, A.: Inseparability criteria based on bipartitions of n-qubit systems. Quantum Inf. Process. 14(3), 979988 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Usha Devi, A.R., Prabhu, R., Rajagopal, A.K.: Characterizing multiparticle entanglement in symmetric n-qubit states via negativity of covariance matrices. Phys. Rev. Lett. 98(6), 060501 (2007)

    Article  Google Scholar 

  20. Bourennane, M., Eibl, M., Kurtsiefer, C., Gaertner, S., Weinfurter, H., Gühne, O., Hyllus, P., Bru”s, D., Lewenstein, M., Sanpera, A.: Experimental detection of multipartite entanglement using witness operators. Phys. Rev. Lett. 92(8), 087902 (2004)

    Article  ADS  Google Scholar 

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

  22. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23(15), 880 (1969)

    Article  ADS  Google Scholar 

  23. Ganguly, N., Adhikari, S., Majumdar, A.S., Chatterjee, J.: Entanglement witness operator for quantum teleportation. Phys. Rev. Lett. 107(27), 270501 (2011)

    Article  Google Scholar 

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Acknowledgements

We acknowledge useful comments from Prof. G. S. Agarwal and Prof. Paul Busch.

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  1. Indian Institute of Science Education And Research Kolkata, Mohanpur, West Bengal, 741 246, India

    Ashutosh K. Goswami & Prasanta K. Panigrahi

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  1. Ashutosh K. Goswami
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  2. Prasanta K. Panigrahi
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Correspondence to Prasanta K. Panigrahi.

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Goswami, A.K., Panigrahi, P.K. Uncertainty Relation and Inseparability Criterion. Found Phys 47, 229–235 (2017). https://doi.org/10.1007/s10701-016-0052-5

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