Skip to main content
SpringerLink
Log in

Characterizing Coherence with Dynamical Entanglement

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

Abstract

Quantum coherence and entanglement are two basic aspects of nonclassicality. With the specific bipartite quantum systems which entanglement and coherence can be calculated, we provide a quantitative connection between the coherence and the dynamical entanglement that be created with the help of incoherent operations. We show that the coherence upper bounds the dynamical entanglement, and in particular conditions of the initial quantum states, the coherence of a single-party is equal to the dynamical entanglement. We extend these results to multipartite quantum systems.

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

Similar content being viewed by others

References

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

    Article  ADS  Google Scholar 

  2. Aberg, J.: Quantifying superposition, arXiv:quant-ph/0612146

  3. Streltsov, A., Adesso, G., Plenio, M.B.: Quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  4. Hu, M.L., Hu, X., Wang, J., Peng, Y., Zhang, Y.R., Fan, H.: Quantum coherence and geometric quantum discord. Phys. Rep. 762, 1 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  6. Bohr, N.: Can quantum-mechanical description of physical reality be considered complete. Phys. Rev. 48, 696 (1935)

    Article  ADS  MATH  Google Scholar 

  7. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Horodecki, M., Oppenheim, J., Winter, A.: Partial quantum information. Nature. 436, 673 (2005)

    Article  ADS  Google Scholar 

  9. Chitambar, E., Hsieh, M.H.: Relating the resource theories of entanglement and quantum coherence. Phys. Rev. Lett. 117, 020402 (2016)

    Article  ADS  Google Scholar 

  10. Streltsov, A., Chitambar, E., Rana, S., Bera, M.N., Winter, A., Lewenstein, M.: Entanglement and coherence in quantum state merging. Phys. Rev. Lett. 116, 240405 (2016)

    Article  ADS  Google Scholar 

  11. Yao, Y., Xiao, X., Ge, L., Sun, C.P.: Quantum coherence in multipartite systems. Phys. Rev. A. 92, 022112 (2015)

    Article  ADS  Google Scholar 

  12. Tan, K.C., Kwon, H., Park, C.Y., Jeong, H.: Unified view of quantum correlations and quantum coherence. Phys. Rev. A. 94, 022329 (2016)

    Article  ADS  Google Scholar 

  13. Zhou, H., Yuan, X., Ma, X.: Unification of quantum resources in distributed scenarios. Phys. Rev. A. 99, 022326 (2019)

    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  MATH  Google Scholar 

  15. Horodecki, M., Horodecki, P., Oppenheim, J.: Reversible transformations from pure to mixed states and the unique measure of information. Phys. Rev. A. 67, 062104 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  16. Gour, G., Spekkens, R.W.: The resource theory of quantum reference frames: manipulations and monotones. New J. Phys. 10, 033023 (2008)

    Article  ADS  Google Scholar 

  17. Brandão, F.G., Horodecki, M., Oppenheim, J., Renes, J.M., Spekkens, R.W.: Resource theory of quantum states out of thermal equilibrium. Phys. Rev. Lett. 111, 250404 (2013)

    Article  ADS  Google Scholar 

  18. Grudka, A., Horodecki, K., Horodecki, M., Horodecki, P., Horodecki, R., Joshi, P., Kłobus, W., Wójcik, A.: Quantifying contextuality. Phys. Rev. Lett. 112, 120401 (2014)

    Article  ADS  Google Scholar 

  19. Zhu, H., Ma, Z., Cao, Z., Fei, S.M., Vedral, V.: Operational one-to-one mapping between coherence and entanglement measures. Phys. Rev. A. 96, 032316 (2017)

    Article  ADS  Google Scholar 

  20. Zhu, H., Hayashi, M., Chen, L.: Coherence and entanglement measures based on Renyi relative entropies. J. Phys. A. 50, 475303 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  21. Zhu, H., Hayashi, M., Chen, L.: Axiomatic and operational connections between the l1-norm of coherence and negativity. Phys. Rev. A. 97, 022342 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  22. Ren, L.H., Gao, M., Ren, J., Wang, Z. D., Bai, Y.K.: Operational resource conversion between coherence and entanglement in multipartite systems. arXiv:2004.03995

  23. Vogel, W., Sperling, J.: Unified quantification of nonclassicality and entanglement. Phys. Rev. A. 89, 052302 (2014)

    Article  ADS  Google Scholar 

  24. Theurer, T., Killoran, N., Egloff, D., Plenio, M.B.: Resource theory of superposition. Phys. Rev. Lett. 119, 230401 (2017)

    Article  ADS  Google Scholar 

  25. Regula, B., Piani, M., Cianciaruso, M., Bromley, T.R., Streltsov, A., Adesso, G.: Converting multilevel nonclassicality into genuine multipartite entanglement. New J. Phys. 20, 033012 (2018)

    Article  ADS  Google Scholar 

  26. Piani, M., Gharibian, S., Adesso, G., Calsamiglia, J., Horodecki, P., Winter, A.: All nonclassical correlations can be activated into distillable entanglement. Phys. Rev. Lett. 106, 220403 (2011)

    Article  ADS  Google Scholar 

  27. Gharibian, S., Piani, M., Adesso, G., Calsamiglia, J., Horodecki, P.: Characterizing quantumness via entanglement creation. Int. J. Quantum. Inform. 9, 1701 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. 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 

  29. Chitambar, E., Streltsov, A., Rana, S., Bera, M.N., Adesso, G., Lewenstein, M.: Assisted distillation of quantum coherence. Phys. Rev. Lett. 116, 070402 (2016)

    Article  ADS  Google Scholar 

  30. Killoran, N., Steinhoff, F.E., Plenio, M.B.: Converting nonclassicality into entanglement. Phys. Rev. Lett. 116, 080402 (2016)

    Article  ADS  Google Scholar 

  31. Ma, J., Yadin, B., Girolami, D., Vedral, V., Gu, M.: Converting coherence to quantum correlations. Phys. Rev. Lett. 116, 160407 (2016)

    Article  ADS  Google Scholar 

  32. Xi, Y., Zhang, T., Zheng, Z.J., Li, X., Fei, S.M.: Converting quantum coherence to genuine multipartite entanglement and nonlocality. Phys. Rev. A. 100, 022310 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  33. Young, J.D., Auyuanet, A.: Entanglement–Coherence and Discord–Coherence analytical relations for X states. Quantum Inf. Process. 19(11), 398 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. Feldman, V., Maziero, J., Auyuanet, A.: Direct-dynamical entanglement-discord relations. Quantum Inf. Process. 16(5), 128 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. Wu, K.D., Hou, Z., Zhong, H.S., Yuan, Y., Xiang, G.Y., Li, C.F., Guo, G.C.: Experimentally obtaining maximal coherence via assisted distillation process. Optica. 4, 454 (2017)

    Article  ADS  Google Scholar 

  36. Wu, K.D., Hou, Z., Zhao, Y.Y., Xiang, G.Y., Li, C.F., Guo, G.C., Ma, J., He,Q.Y., Thompson J., Gu, M.: Experimental cyclic interconversion between coherence and quantum correlations. Phys. Rev. Lett. 121, 050401 (2018)

  37. Qiao, L.F., Streltsov, A., Gao, J., Rana, S., Ren, R.J., Jiao, Z.Q., Hu, C.Q., Xu, X.Y., Wang, C.Y., Tang, H., Yang, A.L., Ma, Z.H., Lewenstein, M., Jin, X.M.: Entanglement activation from quantum coherence and superposition. Phys. Rev. A. 98, 052351 (2018)

    Article  ADS  Google Scholar 

  38. Wang, W., Han, J., Yadin, B., Ma, Y., Ma, J., Cai, W., Xu, Y., Hu, L., Wang, H., Song,Y.P., Gu, M., Sun, L.: Witnessing quantum resource conversion within deterministic quantum computation using one pure superconducting qubit. Phys. Rev. Lett. 123, 220501 (2019)

  39. Theurer, T., Satyajit, S., Plenio, M.B.: Quantifying dynamical coherence with dynamical entanglement. Phys. Rev. Lett. 125, 130401 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  40. Gour, G., Marvian, I., Spekkens, R.W.: Measuring the quality of a quantum reference frame: The relative entropy of frameness. Phys. Rev. A. 80, 012307 (2009)

    Article  ADS  Google Scholar 

  41. Brandão, F.G., Gour, G.: Reversible framework for quantum resource theories. Phys. Rev. Lett. 115, 070503 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  42. Berta, M., Majenz, C.: Disentanglement cost of quantum states. Phys. Rev. Lett. 121, 190503 (2018)

    Article  ADS  Google Scholar 

  43. Groisman, B., Popescu, S., Winter, A.: Quantum, classical, and total amount of correlations in a quantum state. Phys. Rev. A. 72, 032317 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  44. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  45. Yang, L., Xia, Y.: Conditions on coherence converting into entanglement. Chin. Phys. B. 26(8), 080302 (2017)

    Article  ADS  Google Scholar 

  46. Alexander, S., Gerardo, A., Martin, B.P.: Colloquium: Quantum Coherence as a Resource. arXiv: 1609. 02439

  47. Adesso, G., Ambrosio, V., Nagali, E., Piani, M., Sciarrino, F.: Experimental entanglement activation from discord in a programmable quantum measurement. Phys. Rev. Lett. 112, 140501 (2014)

    Article  ADS  Google Scholar 

  48. Horodecki, R., Horodecki, M.: Information-theoretic aspects of inseparability of mixed states. Phys. Rev. A. 54, 1838 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. Werner, R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A. 40, 4277 (1989)

    Article  ADS  MATH  Google Scholar 

  50. Fedrizzi, A.: Experimental distribution of entanglement with separable carriers. Phys. Rev. Lett. 111, 230504 (2013)

    Article  ADS  Google Scholar 

  51. Kay, A.: Using separable Bell-diagonal states to distribute entanglement. Phys. Rev. Lett. 109, 080503 (2012)

    Article  ADS  Google Scholar 

  52. Vedral, V., Plenio, M.B.: Entanglement measures and purification procedures. Phys. Rev. A. 57, 1619 (1998)

    Article  ADS  Google Scholar 

  53. Vicente, J.I., Huber, M.: Multipartite entanglement detection from correlation tensors. Phys. Rev. A. 84, 062306 (2011)

    Article  ADS  Google Scholar 

  54. Huber, M., Sengupta, R.: Witnessing genuine multipartite entanglement with positive maps. Phys. Rev. Lett. 113, 100501 (2014)

    Article  ADS  Google Scholar 

  55. Dai, Y., Dong, Y., Xu, Z., You, W., Zhang, C., Guhne, O.: Experimentally accessible lower bounds for genuine multipartite entanglement and coherence measures. Phys. Rev. Appl. 13, 054022 (2020)

    Article  ADS  Google Scholar 

  56. Szalay, S.: Multipartite entanglement measures. Phys. Rev. A. 92, 042329 (2015)

    Article  ADS  Google Scholar 

  57. Rains, E.: Bound on distillable entanglement. Phys. Rev. A. 60, 179 (1999)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge the financial support by the National Natural Science Foundation (China) under Grant Nos. 61675115, 11647171 and 11574178.

Author information

Authors and Affiliations

  1. School of Physical Science and Intelligent Engineering, Jining University, Qufu, 273155, China

    Lian-Wu Yang & Jie Cheng

  2. Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu, 273165, China

    Zhong-Xiao Man & Yun-Jie Xia

Authors
  1. Lian-Wu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhong-Xiao Man
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yun-Jie Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jie Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lian-Wu Yang.

Ethics declarations

We solemnly declare that the submitted manuscript Characterizing Coherence with Dynamical Entanglement is the result of our work and research. The research results of this manuscript do not contain the contents of any published or unpublished works created by others, except those already cited in the text. Other individuals and groups that have contributed to the research work involved in this manuscript have been clearly identified in the text. We undertake the legal responsibility for the statement of originality of this manuscript.

Competing Interests

The authors declare no conflicts of interest.

Additional information

Publisher’s Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, LW., Man, ZX., Xia, YJ. et al. Characterizing Coherence with Dynamical Entanglement. Int J Theor Phys 62, 84 (2023). https://doi.org/10.1007/s10773-023-05340-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-023-05340-w

Keywords

PACS numbers

Search

Navigation