Skip to main content
SpringerLink
Log in

Quantifying Entanglement with Coherence

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is essentially the normalized coherence of the entangled state in its Schmidt basis. Its value is 1 for maximally entangled states, and 0 for separable states, irrespective of the dimensionality of the Hilbert space. So a maximally entangled state is also the one which is maximally coherent in its Schmidt basis. Quantum entanglement and quantum coherence are thus intimately connected. Entanglement coherence turns out to be closely related to the unified entropy of the reduced state of one of the subsystems. Additionally it is shown that the entanglement coherence is closely connected to the Wigner-Yanase skew information of the reduced density operator of one of the subsystems, in an interesting way.

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

Similar content being viewed by others

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)

    Article  ADS  Google Scholar 

  2. Schrödinger, E.: Die gegenwärtige Situation in der Quantenmechanik. Naturwiss. 23, 807 (1935)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. Paneru, D., Cohen, E., Fickler, R., Boyd, R.W., Karimi, E.: Entanglement: Quantum or classical? Rep. Prog. Phys. 83, 064001 (2020)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  6. 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, 1895 (1993)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  8. Bruß, D.: Characterizing entanglement. J. Math.Phys. 43, 4237 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  9. Plenio, M.B., Virmani, S.S.: Entanglement measures. In: Bruß, D., Leuchs, G. (eds.) Quantum Information. Wiley (2016)

  10. Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  11. Hayden, P.M., Horodecki, M., Terhal, B.M.: The asymptotic entanglement cost of preparing a quantum state. J. Phys. A 34, 6891 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  12. Wang, X., Wilde, M.M.: Cost of quantum entanglement simplified. Phys. Rev. Lett. 040502, 125 (2020)

    MathSciNet  Google Scholar 

  13. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  14. Vedral, V., Plenio, M.B., Rippin, M.A., Knight, P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  15. Plenio, M.B.: Logarithmic negativity: A full entanglement monotone that is not convex. Phys. Rev. Lett. 95, 090503 (2005)

    Article  ADS  Google Scholar 

  16. Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)

    Article  ADS  Google Scholar 

  17. Rungta, P., Buzek, V., Caves, C.M., Hillery, M., Milburn, G.J.: Universal state inversion and concurrence in arbitrary dimensions. Phys. Rev. A 64, 042315 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  18. Bhaskara, V.S., Panigrahi, P.K.: Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using Lagrange’s identity and wedge product. Quantum Inf. Process. 16, 118 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  19. Schmidt, E.: Zur Theorie der linearen und nichtlinearen Integralgleichungen. Math. Ann. 63, 433 (1907)

    Article  MathSciNet  Google Scholar 

  20. Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)

    Article  ADS  Google Scholar 

  21. Qureshi, T.: Coherence, interference and visibility. Quanta 8, 24 (2019)

    Article  MathSciNet  Google Scholar 

  22. Bera, M.N., Qureshi, T., Siddiqui, M.A., Pati, A.K.: Duality of quantum coherence and path distinguishability. Phys. Rev. A 92, 012118 (2015)

    Article  ADS  Google Scholar 

  23. Streltsov, A., Singh, U., Dhar, H.S., Bera, M.N., Adesso, G.: Measuring quantum coherence with entanglement. Phys. Rev. Lett. 115, 020403 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  24. Hu, X., Ye, Z.: Generalized quantum entropy. J. Math. Phys. 47, 023502 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  25. Wigner, E.P., Yanase, M.M.: Information contents of distributions. Proc. Nat. Acad. Sci. USA 49, 910 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  26. Luo, S.: Wigner-Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91, 180403 (2003)

    Article  ADS  Google Scholar 

  27. Banik, M., Deb, P., Bhattacharya, S.: Wigner-Yanase skew information and entanglement generation in quantum measurement. Quantum Inf. Process. 16, 97 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  28. Yu, C.-s., Yang, S.-r., Guo, B.-q.: Total quantum coherence and its applications. Quantum Process. 15, 3773 (2016)

    Article  MathSciNet  Google Scholar 

  29. Luo, S.: Quantum uncertainty of mixed states based on skew information. Phys. Rev. A 73, 022324 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  30. Tóth, G., Moroder, T., Gühne, O.: Evaluating convex roof entanglement measures. Phys. Rev. Lett. 114, 160501 (2015)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

Neha Pathania acknowledges financial support from the Department of Science and Technology, through the Inspire Fellowship (registration code IF180414).

Author information

Authors and Affiliations

  1. Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi, India

    Neha Pathania & Tabish Qureshi

Authors
  1. Neha Pathania
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tabish Qureshi
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Both the authors contributed equally to this work.

Corresponding author

Correspondence to Tabish Qureshi.

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

Pathania, N., Qureshi, T. Quantifying Entanglement with Coherence. Int J Theor Phys 61, 25 (2022). https://doi.org/10.1007/s10773-022-05030-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-022-05030-z

Keywords

Search

Navigation