Skip to main content
SpringerLink
Log in

Enhancing and protecting quantum correlations of a two-qubit entangled system via non-Hermitian operation

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We investigate the dynamics of geometric measure of quantum discord and negativity as a measure of quantum entanglement for the system under the local non-Hermitian operation. Numerical calculations demonstrate that quantum discord and entanglement as two kinds of typical measures of quantum correlations can exceed respective initial value, and their evolution behaviors appear to violate conventional properties which formulates quantum discord and quantum entanglement are invariants under local operations. Our results show that non-Hermitian operation achieves distinctive effects on enhancement and protection of quantum correlations, which is mostly aroused by the non-Hermiticity and the non-unitarity of the non-Hermitian operation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223(1–2), 1–8 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Życzkowski, K., Horodecki, P., Sanpera, A., Lewenstein, M.: Volume of the set of separable states. Phys. Rev. A 58, 883 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  4. Życzkowski, K.: Volume of the set of separable states. II. Phys. Rev. A 60, 3496 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  5. Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  6. Ollivier, H., Zurek, W.H.: Quantum discord: a measurement of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  MATH  Google Scholar 

  7. Dakić, B., Vedral, V., Brukner, Č.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  MATH  Google Scholar 

  8. Breuer, H.-P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  9. Rotter, I.: A non-Hermitian Hamilton operator and the physics of open quantum systems. J. Phys. A: Math. Theor. 42, 153001 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Moiseyev, N.: Non-Hermitian Quantum Mechanics. Cambridge University Press, Cambridge (2011)

    Book  MATH  Google Scholar 

  11. Sergi, A., Zloshchastiev, K.G.: Non-Hermitian quantum dynamics of a two-level system and models of dissipative environments. Int. J. Mod. Phys. B 27, 1350163 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Zloshchastiev, K.G., Sergi, A.: Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems. J. Mod. Opt 61(16), 1298 (2014)

    Article  ADS  Google Scholar 

  13. Bender, C.M., Boettcher, S.: Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80(24), 5243 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Bender, C.M., Brody, D.C., Jones, H.F.: Complex extension of quantum mechanics. Phys. Rev. Lett. 89, 270401 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bender, C.M., Brody, D.C., Jones, H.F., Meister, B.K.: Faster than Hermitian quantum mechanics. Phys. Rev. Lett. 98, 040403 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Günther, U., Samsonov, B.F.: Naimark-dilated PT-symmetric brachistochrone. Phys. Rev. Lett. 101, 230404 (2008)

    Article  MathSciNet  Google Scholar 

  17. Brody, D.C., Graefe, E.-M.: Mixed-state evolution in the presence of gain and loss. Phys. Rev. Lett. 109, 230405 (2012)

    Article  ADS  Google Scholar 

  18. Sergi, A., Zloshchastiev, K.G.: Time correlation functions for non-Hermitian quantum systems. Phys. Rev. A 91, 062108 (2015)

    Article  ADS  Google Scholar 

  19. Konstantin, G.: Zloshchastiev, Non-Hermitian Hamiltonians and stability of pure states. Eur. Phys. J. D 69, 253 (2015)

    Article  Google Scholar 

  20. Sergi, A., Zloshchastiev, K.G.: Quantum entropy of systems described by non-Hermitian Hamiltonians. J. Stat. Mech. 3, 033102 (2016)

    Article  MathSciNet  Google Scholar 

  21. Sergi, A., Giaquinta, P.V.: Linear quantum entropy and non-Hermitian Hamiltonians. Entropy 18, 451 (2016)

    Article  ADS  Google Scholar 

  22. Chen, S.-L., Chen, G.-Y., Chen, Y.-N.: Increase of entanglement by local PT-symmetric operations. Phys. Rev. A 90, 054301 (2014)

    Article  ADS  Google Scholar 

  23. Li, C., Song, Z.: Generation of Bell, W, and Greenberger–Horne–Zeilinger states via exceptional points in non-Hermitian quantum spin systems. Phys. Rev. A 91, 062104 (2015)

    Article  ADS  Google Scholar 

  24. Gardas, B., Deffner, S., Saxena, A.: Non-hermitian quantum thermodynamics. Sci. Rep. 6, 23408 (2016)

    Article  ADS  Google Scholar 

  25. Bagarello, F., Passante, R., Trapani, C.: Non-Hermitian Hamiltonians in quantum physics. Springer, Basel (2015)

    MATH  Google Scholar 

  26. Fernández, Francisco, M.: Non-Hermitian Hamiltonians and similarity transformations. Tnt. J. Theor. Phys. 55(2), 843 (2016)

  27. Ling-Na, W., Jin, G.-R., You, L.: Spin squeezing of the non-Hermitian one-axis twisting model. Phys. Rev. A 92, 033826 (2015)

    Article  ADS  Google Scholar 

  28. Hou, T.-J.: Quantum Fisher information and spin squeezing of the non-Hermitian one-axis twisting model and the effect of dephasing. Phys. Rev. A 95, 013824 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  29. Guo, Y., Fang, M., Wang, G., Hang, J., Zeng, K.: Enhancing parameter estimation precision by non-Hermitian operator process. Quantum Inf. Process 16(12), 301 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Zhang, S.-Y., Fang, M.-F., Xu, S.L.: Quantum entropy of non-Hermitian entangled systems. Quantum Inf. Process 16(10), 234 (2017)

  31. Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)

    Article  ADS  Google Scholar 

  32. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722 (1996)

    Article  ADS  Google Scholar 

  33. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  34. Chang, J., Kwon, Y.: Entanglement behavior of quantum states of fermionic systems in an accelerated frame. Phys. Rev. A 85, 032302 (2012)

    Article  ADS  Google Scholar 

  35. Xiang-Ping, L., Mao-Fa, F., Jian-Shu, F., Qian-Quan, Z.: Preserving entanglement and the fidelity of three-qubit quantum states undergoing decoherence using weak measurement. Chin. Phys. B 23, 020304 (2014)

    Article  Google Scholar 

  36. Nielsenn, M.A., Chuang, I.L.: Quantum Computation and Quantum Information, 10th edn. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  37. Lee, Y.-C., Hsieh, M.-H., Flammia, S.T., Lee, R.-K.: Local PT symmetry violates the no-signaling principle. Phys. Rev. Lett. 112, 130404 (2014)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11374096).

Author information

Authors and Affiliations

  1. Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, College of Physics and Information Science, Hunan Normal University, Changsha, 410081, China

    Yan-Yi Wang & Mao-Fa Fang

  2. Synergetic Innovation Center for Quantum Effects and Applications, College of Physics and Information Science, Hunan Normal University, Changsha, 410081, China

    Yan-Yi Wang & Mao-Fa Fang

Authors
  1. Yan-Yi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mao-Fa Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mao-Fa Fang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, YY., Fang, MF. Enhancing and protecting quantum correlations of a two-qubit entangled system via non-Hermitian operation. Quantum Inf Process 17, 208 (2018). https://doi.org/10.1007/s11128-018-1977-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-1977-8

Keywords

Search

Navigation