Frontiers of Physics

, 13:130701 | Cite as

Quantifying quantum correlation via quantum coherence

  • Guang-Yong Zhou
  • Lin-Jian Huang
  • Jun-Ya Pan
  • Li-Yun Hu
  • Jie-Hui HuangEmail author
Research Article


Resource theory is applied to quantify the quantum correlation of a bipartite state and a computable measure is proposed. Since this measure is based on quantum coherence, we present another possible physical meaning for quantum correlation, i.e., the minimum quantum coherence achieved under local unitary transformations. This measure satisfies the basic requirements for quantifying quantum correlation and coincides with concurrence for pure states. Since no optimization is involved in the final definition, this measure is easy to compute irrespective of the Hilbert space dimension of the bipartite state.


resource theory quantum correlation quantum coherence 



This work was supported by the national Natural Science Foundation of China under Grant Nos. 11664018 and 11664017.


  1. 1.
    E. Knill and R. Laflamme, Power of one bit of quantum information, Phys. Rev. Lett. 81(25), 5672 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    A. Datta, A. Shaji, and C. M. Caves, Quantum discord and the power of one qubit, Phys. Rev. Lett. 100(5), 050502 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    B. P. Lanyon, M. Barbieri, M. P Almeida, and A. G. White, Experimental quantum computing without entanglement, Phys. Rev. Lett. 101(20), 200501 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    H. Ollivier and W. H. Zurek, Quantum discord: A measure of the quantumness of correlations, Phys. Rev. Lett. 88(1), 017901 (2001)ADSzbMATHCrossRefGoogle Scholar
  5. 5.
    G. Gour and R. W. Spekkens, The resource theory of quantum reference frames: Manipulations and monotones, New J. Phys. 10(3), 033023 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    F. G. S. L. Brandão and G. Gour, Reversible framework for quantum resource theories, Phys. Rev. Lett. 115(7), 070503 (2015)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    B. Coecke, T. Fritz, and R. W. Spekkens, A mathematical theory of resources, Inf. Comput. 250, 59 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    R. Demkowicz-Dobrzanski and L. Maccone, Using entanglement against noise in quantum metrology, Phys. Rev. Lett. 113(25), 250801 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    J. Åberg, Catalytic coherence, Phys. Rev. Lett. 113(15), 150402 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    V. Narasimhachar and G. Gour, Low-temperature thermodynamics with quantum coherence, Nat. Commun. 6(1), 7689 (2015)ADSCrossRefGoogle Scholar
  11. 11.
    P. Cwiklinski, M. Studzinski, M. Horodecki, and J. Oppenheim, Limitations on the evolution of quantum coherences: Towards fully quantum second laws of thermodynamics, Phys. Rev. Lett. 115(21), 210403 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    M. Lostaglio, D. Jennings, and T. Rudolph, Description of quantum coherence in thermodynamic processes requires constraints beyond free energy, Nat. Commun. 6(1), 6383 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    M. Lostaglio, K. Korzekwa, D. Jennings, and T. Rudolph, Quantum coherence, time-translation symmetry, and thermodynamics, Phys. Rev. X 5(2), 021001 (2015)CrossRefGoogle Scholar
  14. 14.
    I. Marvian and R. W. Spekkens, Extending Noether’s theorem by quantifying the asymmetry of quantum states, Nat. Commun. 5(1), 3821 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    F. Levi and F. Mintert, A quantitative theory of coherent delocalization, New J. Phys. 16(3), 033007 (2014)ADSCrossRefGoogle Scholar
  16. 16.
    L. M. Yang, B. Chen, S. M. Fei, and Z. X. Wang, Dynamics of coherence-induced state ordering under Markovian channels, Front. Phys. 13(5), 130310 (2018)CrossRefGoogle Scholar
  17. 17.
    T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying coherence, Phys. Rev. Lett. 113(14), 140401 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    X. D. Yu, D. J. Zhang, G. F. Xu, and D. M. Tong, Alternative framework for quantifying coherence, Phys. Rev. A 94(6), 060302(R) (2016)CrossRefGoogle Scholar
  19. 19.
    X. Yuan, H. Zhou, Z. Cao, and X. Ma, Intrinsic randomness as a measure of quantum coherence, Phys. Rev. A 92(2), 022124 (2015)ADSCrossRefGoogle Scholar
  20. 20.
    A. Winter and D. Yang, Operational resource theory of coherence, Phys. Rev. Lett. 116(12), 120404 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    Y. Yao, X. Xiao, L. Ge, and C. P. Sun, Quantum coherence in multipartite systems, Phys. Rev. A 92(2), 022112 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    Z. Xi, Y. Li, and H. Fan, Quantum coherence and correlations in quantum system, Sci. Rep. 5(1), 10922 (2015)ADSCrossRefGoogle Scholar
  23. 23.
    J. Ma, B. Yadin, D. Girolami, V. Vedral, and M. Gu, Converting coherence to quantum correlations, Phys. Rev. Lett. 116(16), 160407 (2016)ADSCrossRefGoogle Scholar
  24. 24.
    C. Radhakrishnan, M. Parthasarathy, S. Jambulingam, and T. Byrnes, Distribution of quantum coherence in multipartite systems, Phys. Rev. Lett. 116(15), 150504 (2016)ADSCrossRefGoogle Scholar
  25. 25.
    T. R. Bromley, M. Cianciaruso, and G. Adesso, Frozen quantum coherence, Phys. Rev. Lett. 114(21), 210401 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    X. D. Yu, D. J. Zhang, C. L. Liu, and D. M. Tong, Measure-independent freezing of quantum coherence, Phys. Rev. A 93(6), 060303 (2016)CrossRefGoogle Scholar
  27. 27.
    E. Chitambar, A. Streltsov, S. Rana, M. N. Bera, G. Adesso, and M. Lewenstein, Assisted distillation of quantum coherence, Phys. Rev. Lett. 116(7), 070402 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    R. A. Horn and C. R. Johnson, Matrix Analysis, Chaps. 2, 5 and 7, New York: Cambridge University Press, 1985CrossRefGoogle Scholar
  29. 29.
    A. Brodutch and K. Modi, Criteria for measures of quantum correlations, Quantum Inf. Comput. 12, 721 (2012)MathSciNetzbMATHGoogle Scholar
  30. 30.
    W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80(10), 2245 (1998)ADSzbMATHCrossRefGoogle Scholar
  31. 31.
    P. Rungta, V. Bužek, C. M. Caves, M. Hillery, and G. J. Milburn, Universal state inversion and concurrence in arbitrary dimensions, Phys. Rev. A 64(4), 042315 (2001)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    E. Chitambar and M. H. Hsieh, Relating the resource theories of entanglement and quantum coherence, Phys. Rev. Lett. 117(2), 020402 (2016)ADSCrossRefGoogle Scholar
  33. 33.
    A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Measuring quantum coherence with entanglement, Phys. Rev. Lett. 115(2), 020403 (2015)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    J. J. Ma, B. Yadin, D. Girolami, V. Vedral, and M. Gu, Converting coherence to quantum correlations, Phys. Rev. Lett. 116(16), 160407 (2016)ADSCrossRefGoogle Scholar
  35. 35.
    B. Dakić, V. Vedral, and Ç. Brukner, Necessary and sufficient condition for nonzero quantum discord, Phys. Rev. Lett. 105(19), 190502 (2010)ADSzbMATHCrossRefGoogle Scholar
  36. 36.
    J. H. Huang, L. Wang, and S. Y. Zhu, A new criterion for zero quantum discord, New J. Phys. 13(6), 063045 (2011)ADSCrossRefGoogle Scholar
  37. 37.
    L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80(2), 517 (2008)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81(2), 865 (2009)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    K. Modi, T. Paterek, W. Son, V. Vedral, and M. Williamson, Unified view of quantum and classical correlations, Phys. Rev. Lett. 104(8), 080501 (2010)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    C. C. Rulli and M. S. Sarandy, Global quantum discord in multipartite systems, Phys. Rev. A 84(4), 042109 (2011)ADSCrossRefGoogle Scholar
  41. 41.
    J. Batle, A. Farouk, O. Tarawneh, and S. Abdalla, Multipartite quantum correlations among atoms in QED cavities, Front. Phys. 13(1), 130305 (2018)CrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Guang-Yong Zhou
    • 1
  • Lin-Jian Huang
    • 1
  • Jun-Ya Pan
    • 1
  • Li-Yun Hu
    • 1
  • Jie-Hui Huang
    • 1
    Email author
  1. 1.College of Physics and Communication ElectronicsJiangxi Normal UniversityNanchangChina

Personalised recommendations