Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Observing the operational significance of discord consumption

Abstract

Coherent interactions that generate negligible entanglement can still exhibit unique quantum behaviour. This observation has motivated a search beyond entanglement for a complete description of all quantum correlations. Quantum discord is a promising candidate. Here, we demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interactions. The inability to access this information by any other means allows us to use discord to directly quantify this ‘quantum advantage’. We experimentally encode information within the discordant correlations of two separable Gaussian states. The amount of extra information recovered by coherent interaction is quantified and directly linked with the discord consumed during encoding. No entanglement exists at any point of this experiment. Thus we introduce and demonstrate an operational method to use discord as a physical resource.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Experimental implementation of the discord consumption protocol in continuous variables.
Figure 2: Plot of Bob’s knowledge of the encoded signal for bipartite resource states with varying discording noise and fixed encoding variance Vs.
Figure 3: Plot of quantum advantage for a fixed resource state (with V = 10.0±0.1) with varying strength of the the encoded signal, Vs.

References

  1. Bennett, C. H. & Wiesner, S. J. Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992).

    ADS  MathSciNet  Article  Google Scholar 

  2. Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997).

    MathSciNet  Article  Google Scholar 

  3. Ekert, A. K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991).

    ADS  MathSciNet  Article  Google Scholar 

  4. Grover, L. K. Quantum Mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997).

    ADS  Article  Google Scholar 

  5. Bennett, C. H. & Brassard, G. Proc. IEEE Int. Conf. on Computers, Systems and Signal Processing 175–179 (IEEE, 1984).

    Google Scholar 

  6. Knill, E. & Laflamme, R. Power of one bit of quantum information. Phys. Rev. Lett. 81, 5672–5675 (1998).

    ADS  Article  Google Scholar 

  7. Datta, A. & Vidal, G. Role of entanglement and correlations in mixed-state quantum computation. Phys. Rev. A 75, 042310 (2007).

    ADS  MathSciNet  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  9. Lanyon, B. P., Barbieri, M., Almeida, M. P. & White, A. G. Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008).

    ADS  Article  Google Scholar 

  10. Bennett, C. H. et al. Quantum nonlocality without entanglement. Phys. Rev. A 59, 1070–1091 (1999).

    ADS  MathSciNet  Article  Google Scholar 

  11. Henderson, L. & Vedral, V. Classical, quantum and total correlations. J. Phys. A 34, 6899–6905 (2001).

    ADS  MathSciNet  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  13. Laflamme, R., Cory, D. G., Negrevergne, C. & Viola, L. NMR quantum information processing and entanglement. Quant. Inf. Comput. 2, 166–176 (2002).

    MathSciNet  MATH  Google Scholar 

  14. Vedral, V. The elusive source of quantum speedup. Found. Phys. 40, 1141–1154 (2010).

    ADS  MathSciNet  Article  Google Scholar 

  15. Rodríguez-Rosario, C. A., Modi, K., Kuah, A.-M., Shaji, A. & Sudarshan, E. C. G. Completely positive maps and classical correlations. J. Phys. A 41, 205301 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  16. Piani, M., Horodecki, P. & Horodecki, R. No-local-broadcasting theorem for quantum correlations. Phys. Rev. Lett. 100, 090502 (2008).

    ADS  Article  Google Scholar 

  17. Luo, S. & Sun, W. Decomposition of bipartite states with applications to quantum no-broadcasting theorems. Phys. Rev. A 82, 012338 (2010).

    ADS  Article  Google Scholar 

  18. Tomasello, B., Rossini, D., Hamma, A. & Amico, L. Symmetry breaking and correlations in a quantum many body system. Europhys. Lett. 96, 27002 (2011).

    ADS  Article  Google Scholar 

  19. Giorda, P. & Paris, M. G. A. Gaussian quantum discord. Phys. Rev. Lett. 105, 020503 (2010).

    ADS  Article  Google Scholar 

  20. Adesso, G. & Datta, A. Quantum versus classical correlations in Gaussian states. Phys. Rev. Lett. 105, 030501 (2010).

    ADS  Article  Google Scholar 

  21. Oppenheim, J., Horodecki, M., Horodecki, P. & Horodecki, R. A thermodynamical approach to quantifying quantum correlations. Phys. Rev. Lett. 89, 180402 (2002).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  23. Brodutch, A. & Terno, D. R. Quantum discord and local demons. Phys. Rev. A 81, 062103 (2010).

    ADS  MathSciNet  Article  Google Scholar 

  24. Datta, A. & Gharibian, S. Signatures of non-classicality in mixed-state quantum computation. Phys. Rev. A 79, 042325 (2009).

    ADS  Article  Google Scholar 

  25. Boixo, S., Aolita, L., Cavalcanti, D., Modi, K. & Winter, A. Quantum locking of classical correlations and quantum discord of classical-quantum states. IJQI 9, 1643–1651 (2011).

    MathSciNet  MATH  Google Scholar 

  26. Cavalcanti, D. et al. Operational interpretations of quantum discord. Phys. Rev. A 83, 032324 (2011).

    ADS  Article  Google Scholar 

  27. Madhok, V. & Datta, A. Interpreting quantum discord through quantum state merging. Phys. Rev. A 83, 032323 (2011).

    ADS  Article  Google Scholar 

  28. Madhok, V. & Datta, A. Lecture Notes in Computer Science (Springer, 2011).

    Google Scholar 

  29. Braunstein, S. L., Cerf, N. J., Iblisdir, S., van Loock, P. & Massar, S. Optimal cloning of coherent states with a linear amplifier and beam splitters. Phys. Rev. Lett. 86, 4938–4941 (2001).

    ADS  Article  Google Scholar 

  30. Fiurášek, J. Optical implementation of continuous-variable quantum cloning machines. Phys. Rev. Lett. 86, 4942–4945 (2001).

    ADS  Article  Google Scholar 

  31. Weedbrook, C. et al. Gaussian quantum information. Rev. Mod. Phys. 84, 621–669.

    ADS  Article  Google Scholar 

  32. Schumacher, B. & Westmoreland, M. D. Quantum mutual information and the one-time pad. Phys. Rev. A 74, 042305 (2006).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank C. Weedbrook, J. Thompson, N. Walk and H. Wiseman for helpful discussions. The research is supported by the National Research Foundation and Ministry of Education in Singapore (M.G., K.M. and V.V.), the John Templeton Foundation (K.M. and V.V.), and the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (Project number CE110001027). (H.C., S.M.A., T.S., T.C.R. and P.K.L.).

Author information

Authors and Affiliations

Authors

Contributions

M.G. V.V. and T.C.R. conceived the idea. M.G. and K.M. formalized the theory. P.K.L., M.G., T.S., S.M.A. and H.M.C. conceived the experiment. H.M.C. and S.M.A. conducted the experiment and analysed the data. S.M.A. and H.M.C. developed the experimental model. M.G., H.M.C, T.S. and S.M.A. drafted the manuscript. P.K.L, T.S. and V.V. planned and supervised the project. All authors discussed the results and commented on the manuscript at all stages.

Corresponding authors

Correspondence to Mile Gu or Ping Koy Lam.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 257 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gu, M., Chrzanowski, H., Assad, S. et al. Observing the operational significance of discord consumption. Nature Phys 8, 671–675 (2012). https://doi.org/10.1038/nphys2376

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys2376

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing