Skip to main content
Log in

Information gain and systems entanglement in tripartite measurement model

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

It is well known that obtaining information of the quantum system can be performed by quantum measurements. However, it also brings disturbance to the system and affects the entanglement between arbitrary bipartite systems. Firstly, based on the introduction of the purification system, the measurement process has been modeled as the tripartite systems. Then, the definitions of various information quantities are provided. Finally, we discuss the relationships between information gain and entanglement in the tripartite systems.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Kraus, K.: States, Effects, and Operations: Fundamental Notions of Quantum Theory. Springer, Berlin (1983)

    Book  Google Scholar 

  2. Nielsen, M.A., Caves, C.M.: Reversible quantum operations and their application to teleportation. Phys. Rev. A 55, 2547 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  3. Fuchs, C.A., Jacobs, K.: Information tradeoff relations for finite-strength quantum measurements. Phys. Rev. A 63, 062305 (2001)

    Article  ADS  Google Scholar 

  4. Vedral, V.: The role of relative entropy in quantum information theory. Rev. Mod. Phys. 74, 197 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  5. Jacobs, K.: Efficient measurements, purification, and bounds on the mutual information. Phys. Rev. A 68, 054302 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  6. Roga, W., Fannes, M., Zyczkowski, K.: Universal bounds for the Holevo quantity, coherent information, and the Jensen–Shannon divergence. Phys. Rev. Lett. 105, 040505 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  7. Luo, S.L.: Information conservation and entropy change in quantum measurements. Phys. Rev. A 82, 052103 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  8. Duan, Z.B., Hou, J.C.: Entropy change in quantum measurements for infinite-dimensional quantum systems. Int. J. Theor. Phys. 58, 463 (2019)

    Article  Google Scholar 

  9. Groenewold, H.J.: A problem of information gain by quantal measurements. Int. J. Theor. Phys. 4, 327 (1971)

    Article  Google Scholar 

  10. Ozawa, M.: On information gain by quantum measurements of continuous observables. J. Math. Phys. 27, 759 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  11. Fuchs, C.A.: Information gain vs. state disturbance in quantum theory. Fortschr. Phys. 46, 4 (1996)

    MathSciNet  Google Scholar 

  12. Schumacher, B., Nielsen, M.A.: Quantum data processing and error correction. Phys. Rev. A 54, 2629 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  13. Schumacher, B.: Sending entanglement through noisy quantum channels. Phys. Rev. A 54, 2614 (1996)

    Article  ADS  Google Scholar 

  14. Adami, C., Cerf, N.J.: On the von Neumann capacity of noisy quantum channels. Phys. Rev. A 56, 3470 (1996)

    Article  ADS  Google Scholar 

  15. Maccone, L.: Entropic information-disturbance tradeoff. Europhys. Lett. 77, 40002 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  16. Buscemi, F., Hayashi, M., Horodecki, M.: Global information balance in quantum measurements. Phys. Rev. Lett. 100, 210504 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  17. Fuchs, C.A., Peres, A.: Quantum-state disturbance versus information gain: uncertainty relations for quantum information. Phys. Rev. A 53, 2038 (1996)

    Article  ADS  Google Scholar 

  18. Ban, M.: State reduction, information and entropy in quantum measurement processes. Phys. A Gen. Phys. 32, 1643 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  19. Sacchi, M.F.: Information-disturbance tradeoff in estimating a maximally entangled state. Phys. Rev. Lett. 96, 220502 (2006)

    Article  ADS  Google Scholar 

  20. Shirokov, M.E.: Entropy reduction of quantum measurements. J. Math. Phys. 52, 052202 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  21. Heinosaari, T., Miyadera, T.: Qualitative noise-disturbance relation for quantum measurements. Phys. Rev. A 88, 042117 (2013)

    Article  ADS  Google Scholar 

  22. Buscemi, M.F., Hall, J.W., Ozawa, M., et al.: Noise and disturbance in quantum measurements: an information-theoretic approach. Phys. Rev. Lett. 112, 050401 (2014)

    Article  ADS  Google Scholar 

  23. Xi, Z.J.: Information gain and information leak in quantum measurements. Phys. Rev. A 93, 052308 (2016)

    Article  ADS  Google Scholar 

  24. Vedral, V.: Classical correlations and entanglement in quantum measurements. Phys. Rev. Lett. 90, 050401 (2003)

    Article  ADS  Google Scholar 

  25. Koashi, M., Winter, A.: Monogamy of entanglement and other correlations. Phys. Rev. A 69, 022309 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  26. Sun, Q.Q., Al-Amri, D.M., Davidovich, L., et al.: Reversing entanglement change by a weak measurement. Phys. Rev. A 82, 052323 (2010)

    Article  ADS  Google Scholar 

  27. Luo, S.L., Li, N.: Decoherence and measurement-induced correlations. Phys. Rev. A 84, 052309 (2011)

    Article  ADS  Google Scholar 

  28. Piani, M., Adesso, G.: Quantumness versus entanglement in quantum measurements. Phys. Rev. A 85, 040301 (2011)

    Article  Google Scholar 

  29. Hu, M.L., Fan, H.: Competition between quantum correlations in the quantum-memory-assisted entropic uncertainty relation. Phys. Rev. A 87, 022314 (2013)

    Article  ADS  Google Scholar 

  30. Adesso, G., Bromley, T.R., Cianciaruso, M.: Measures and applications of quantum correlations. J. Phys. A Math. Theor. 49, 473001 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  31. Hu, M.L., Hu, X.Y., Wang, J.C., et al.: Quantum coherence and geometric quantum discord. Phys. Rep. 762–764, 1–100 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  32. Fujikawa, K., Oh, C.H., Umetsu, K.: A classical limit of Grover’s algorithm induced by dephasing: coherence versus entanglement. Mod. Phys. Lett. A 34, 1950146 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  33. Gordon, J.P.: Noise at optical frequencies; information theory quantumn electronics and coherent light. In: Miles, P.A. (ed.), Proceedings of the International School of Physics, Academic Press, New York, pp. 156–181 (1964)

  34. Holevo, A.S.: Statistical problems in quantum physics. In: Maruyama, G., Prokhorov, J.N. (eds.) Proceedings of the Second Japan-USSR Symposium on Probability Theory, Lecture Notes in Mathematics, Springer, Berlin, pp. 104–119 (1973)

  35. Lindblad, G.: Quantum entropy and quantum measurements. In: Bendjiaballh, C., Hirota, O., Reynaud, S.(eds.) Lecture Notes in Physics, Springer, Berlin, pp. 19–80 (1991)

  36. Lloyd, S.: Capacity of the noisy quantum channel. Phys. Rev. A 55, 1613 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  37. Roga, W.: Entropy of quantum channel in the theory of quantum information. arXiv: quant-ph/1108.5065 (2011)

  38. Plenio, M.B., Vedral, V.: Bounds on relative entropy of entanglement for multi-party systems. Phys. A Gen. Phys. 34, 6997 (2001)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11671284), Sichuan Science and Technology Program (Grant No. 2020YFG0290).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ming-qiang Bai.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Wj., Tang, L., Zhang, Q. et al. Information gain and systems entanglement in tripartite measurement model. Quantum Inf Process 20, 38 (2021). https://doi.org/10.1007/s11128-020-02979-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02979-w

Keywords

Navigation