Skip to main content
SpringerLink
Log in

Information-based approach towards a unified resource theory

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Resource theories play an important role in quantum information theory, as they identify resourceful states and channels that are potentially useful for the accomplishment of tasks that would be otherwise unreachable. The elementary structure of such theories, which is based on the definition of free states and free operations, successfully accommodates different nonclassical aspects, such as quantum coherence and entanglement, but it is still not clear whether and how far such formal framework can be extended. In this work, by taking information as the most primitive quantum resource and defining resource-destroying operations, we develop a unifying approach that proves able to encompass several nonclassical aspects, including the newly developed concepts of quantum irreality and realism-based nonlocality.

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. Chitambar, E., Gour, G.: Quantum resource theories. Rev. Mod. Phys. 91, 025001 (2019)

    ADS  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

  3. 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)

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  5. Winter, A., Yang, D.: Operational resource theory of coherence. Phys. Rev. Lett. 116, 120404 (2016)

    ADS  Google Scholar 

  6. Gour, G., Müller, M.P., Narasimhachar, V., Spekkens, R.W., Halpern, N.Y.: The resource theory of informational nonequilibrium in thermodynamics. Phys. Rep. 583, 1 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  7. Goold, J., Huber, M., Riera, A., del Rio, L., Skrzypczyk, P.: The role of quantum information in thermodynamics: a topical review. J. Phys. A 49, 143001 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  9. Horodecki, M., Oppenheim, J.: Quantumness in the context of resource theories. Int. J. Mod. Phys. B 27, 1345019 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  10. Coecke, B., Fritz, T., Spekkens, R.W.: A mathematical theory of resources. Inf. Comput. 250, 59 (2016)

    MathSciNet  MATH  Google Scholar 

  11. Liu, Z.-W., Hu, X., Lloyd, S.: Resource-destroyingMaps. Phys. Rev. Lett. 118, 060502 (2017)

    ADS  Google Scholar 

  12. Takagi, R., Regula, B., Bu, K., Liu, Z.-W., Adesso, G.: Operational advantage of quantum resources in subchannel discrimination. Phys. Rev. Lett. 122, 140402 (2019)

    ADS  Google Scholar 

  13. Takagi, R., Regula, B.: General resource theories in quantum mechanics and beyond: operational characterization via discrimination tasks. Phys. Rev. X 9, 031053 (2019)

    Google Scholar 

  14. Bilobran, A.L.O., Angelo, R.M.: A measure of physical reality. Europhys. Lett. 112, 40005 (2015)

    ADS  Google Scholar 

  15. Gomes, V.S., Angelo, R.M.: Nonanomalous realism-based measure of nonlocality. Phys. Rev. A 97, 012123 (2018)

    ADS  Google Scholar 

  16. Gomes, V.S., Angelo, R.M.: Resilience of realism-based nonlocality to local disturbance. Phys. Rev. A 99, 012109 (2019)

    ADS  Google Scholar 

  17. Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J., Sen(De), A., Sen, U., Synak-Radtke, B.: Local versus nonlocal information in quantum-information theory: formalism and phenomena. Phys. Rev. A 71, 062307 (2005)

    ADS  MATH  Google Scholar 

  18. Streltsov, A., Kampermann, H., Wölk, S., Gessner, M., Bruß, D.: Maximal coherence and the resource theory of purity. New J. Phys. 20, 053058 (2018)

    ADS  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  21. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    ADS  MATH  Google Scholar 

  22. Pironio, S., Acín, A., Massar, S., Boyer de la Giroday, A., Matsukevich, D.N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T.A., Monroe, C.: Random numbers certified by Bell’s theorem. Nature 464, 1021 (2010)

    ADS  Google Scholar 

  23. Toth, G., Apellaniz, I.: Quantum metrology from a quantum information science perspective. J. Phys. A Math. Theor. 47, 424006 (2014)

    ADS  MathSciNet  MATH  Google Scholar 

  24. 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)

    ADS  MathSciNet  MATH  Google Scholar 

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

    ADS  MATH  Google Scholar 

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

    ADS  MATH  Google Scholar 

  27. Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Math. Gen. 34, 6899 (2001)

    ADS  MathSciNet  MATH  Google Scholar 

  28. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)

    ADS  Google Scholar 

  29. Dakić, B., Lipp, Y.O., Ma, X., Ringbauer, M., Kropatschek, S., Barz, S., Paterek, T., Vedral, V., Zeilinger, A., Brukner, Č., Walther, P.: Quantum discord as resource for remote state preparation. Nat. Phys. 8, 666 (2012)

    Google Scholar 

  30. Madhok, V., Datta, A.: Quantum discord as a resource in quantum communication. Int. J. Mod. Phys. B 27, 1345041 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  31. Pirandola, S.: Quantum discord as a resource for quantum cryptography. Sci. Rep. 4, 6956 (2014)

    ADS  Google Scholar 

  32. Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011)

    ADS  Google Scholar 

  33. Xi, Z., Lu, X.-M., Wang, X., Li, Y.: Necessary and sufficient condition for saturating the upper bound of quantum discord. Phys. Rev. A 85, 032109 (2012)

    ADS  Google Scholar 

  34. Xi, Z., Lu, X.-M., Wang, X., Li, Y.: The upper bound and continuity of quantum discord. J. Phys. A Math. Theor. 44, 375301 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  35. Dieguez, P.R., Angelo, R.M.: Weak quantum discord. Quantum Inf. Process. 17, 194 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  36. Dieguez, P.R., Angelo, R.M.: Information-reality complementarity: the role of measurements and quantum reference frames. Phys. Rev. A 97, 022107 (2018)

    ADS  Google Scholar 

  37. Freire, I.S., Angelo, R.M.: Quantifying continuous-variable realism. Phys. Rev. A 100, 022105 (2019)

    ADS  Google Scholar 

  38. Orthey, A.C., Angelo, R.M.: Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers. Phys. Rev. A 100, 042110 (2019)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  40. Streltsov, A., Rana, S., Bera, M.N., Lewenstein, M.: Towards resource theory of coherence in distributed scenarios. Phys. Rev. X 7, 011024 (2017)

    Google Scholar 

  41. Zurek, W.H.: Quantum discord and Maxwell’s demons. Phys. Rev. A 67, 012320 (2003)

    ADS  Google Scholar 

  42. Costa, A.C.S., Angelo, R.M.: Bayes’ rule, generalized discord, and nonextensive thermodynamics. Phys. Rev. A 87, 032109 (2013)

    ADS  Google Scholar 

  43. Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)

    ADS  MathSciNet  Google Scholar 

  44. Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)

    ADS  Google Scholar 

  45. Lami, L., Regula, B., Adesso, G.: Generic bound coherence under strictly incoherent operations. Phys. Rev. Lett. 122, 150402 (2019)

    ADS  Google Scholar 

  46. Lami, L.: Completing the grand tour of asymptotic quantum coherence manipulation. IEEE Trans. Inf. Theory 66, 2165–2183 (2019)

    ADS  Google Scholar 

Download references

Acknowledgements

A.C.S.C. acknowledges CAPES/Brazil and CNPq/Brazil (Grant Number: 153436/2018-2). R.M.A. acknowledges support from CNPq/Brazil (Grant Number: 303111/2017-8) and the National Institute for Science and Technology of Quantum Information (CNPq, INCT-IQ 465469/2014-0).

Author information

Authors and Affiliations

  1. Department of Physics, Federal University of Paraná, P.O. Box 19044, Curitiba, Paraná, 81531-980, Brazil

    A. C. S. Costa & R. M. Angelo

Authors
  1. A. C. S. Costa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. M. Angelo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. C. S. Costa.

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

Costa, A.C.S., Angelo, R.M. Information-based approach towards a unified resource theory. Quantum Inf Process 19, 325 (2020). https://doi.org/10.1007/s11128-020-02826-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02826-y

Keywords

Search

Navigation