Skip to main content

Thank you for visiting 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.

Quantum discord as resource for remote state preparation


The existence of better-than-classical quantum information processing (QIP) models which consume very little or no entanglement suggests that separable or weakly entangled states could be extremely useful tools for information processing as they are much easier to prepare and control even in dissipative environments. It has been proposed that a resource of advantage is the generation of quantum discord, a measure of non-classical correlations that includes entanglement as a subset. Here we show that quantum discord is the necessary resource for quantum remote state preparation. We explicitly show that the geometric measure of quantum discord is related to the fidelity of this task, which provides its operational meaning. Our results are experimentally demonstrated using photonic quantum systems. Moreover, we demonstrate that separable states with non-zero quantum discord can outperform entangled states. Therefore, the role of quantum discord might provide fundamental insights for resource-efficient QIP.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Figure 1: RSP.
Figure 2: Experimental set-up to realize the RSP protocol.
Figure 3: Experimentally achieved RSP-payoff for 58 distinct states on Bob’s Bloch sphere.


  1. Schrödinger, E. Discussion of probability relations between separated systems. Math. Proc. Cambridge Phil. Soc. 31, 555–563 (1935).

    Article  ADS  Google Scholar 

  2. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

    MATH  Google Scholar 

  3. Buhrman, H., Cleve, R., Massar, S. & de Wolf, R. Nonlocality and communication complexity. Rev. Mod. Phys. 82, 665–698 (2010).

    Article  ADS  Google Scholar 

  4. Brukner, Č., Zukowski, M., Pan, J-W. & Zeilinger, A. Bell’s inequalities and quantum communication complexity. Phys. Rev. Lett. 92, 127901–127905 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  5. Ekert, A. K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–665 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  6. Monz, T. et al. 14-qubit entanglement: Creation and coherence. Phys. Rev. Lett. 106, 130506–130510 (2011).

    Article  ADS  Google Scholar 

  7. Yao, X. et al. Observation of eight-photon entanglement. Nature Photon. 6, 225–228 (2012).

    Article  ADS  Google Scholar 

  8. Huang, Y. et al. Experimental generation of an eight-photon Greenberger–Horne–Zeilinger state. Nature Commun. 2, 546–552 (2011).

    Article  Google Scholar 

  9. Jozsa, R. & Linden, N. On the role of entanglement in quantum-computational speed-up. Proc. R. Soc. Lond. Ser. A 459, 2011–2032 (2003).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Meyer, D. A. Sophisticated quantum search without entanglement. Phys. Rev. Lett. 85, 2014–2017 (2000).

    Article  ADS  Google Scholar 

  12. Ryan, C. A., Emerson, J., Poulin, D., Negrevergne, C. & Laflamme, R. Characterization of complex quantum dynamics with a scalable NMR information processor. Phys. Rev. Lett. 95, 250502–250507 (2005).

    Article  ADS  Google Scholar 

  13. Lanyon, B. P., Barbieri, M., Almeida, M. P. & White, A. G. Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501–200505 (2008).

    Article  ADS  Google Scholar 

  14. Passante, G., Moussa, O., Trottier, D. A. & Laflamme, R. Experimental detection of nonclassical correlations in mixed-state quantum computation. Phys. Rev. A 84, 044302–044306 (2011).

    Article  ADS  Google Scholar 

  15. Ollivier, H. & Zurek, W. H. Quantum discord: A measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901–017905 (2001).

    Article  ADS  Google Scholar 

  16. Zurek, W. H. Einselection and decoherence from an information theory perspective. Annalen der Physik 512, 855–864 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  17. Henderson, L. & Vedral, V. Classical, quantum and total correlations. J. Phys. A 34, 6899–6909 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  18. Datta, A., Shaji, A. & Caves, C. M. Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502–050507 (2008).

    Article  ADS  Google Scholar 

  19. Cavalcanti, D. et al. Operational interpretations of quantum discord. Phys. Rev. A 83, 032324–032329 (2011).

    Article  ADS  Google Scholar 

  20. Madhok, V. & Datta, A. Interpreting quantum discord through quantum state merging. Phys. Rev. A 83, 032323–032327 (2011).

    Article  ADS  Google Scholar 

  21. Madhok, V. & Datta, A. Role of quantum discord in quantum communication. Preprint at (2011).

  22. Piani, M., Horodecki, P. & Horodecki, R. No-local-broadcasting theorem for multipartite quantum correlations. Phys. Rev. Lett. 100, 090502–090507 (2008).

    Article  ADS  Google Scholar 

  23. Roa, L., Retamal, J. C. & Alid-Vaccarezza, M. Dissonance is required for assisted optimal state discrimination. Phys. Rev. Lett. 107, 080401–080405 (2011).

    Article  ADS  Google Scholar 

  24. Datta, A., Flammia, S. T. & Caves, C. M. Entanglement and the power of one qubit. Phys. Rev. A 72, 042316–042330 (2005).

    Article  ADS  Google Scholar 

  25. Braunstein, S. L. et al. Separability of very noisy mixed states and implications for NMR quantum computing. Phys. Rev. Lett. 83, 1054–1057 (1999).

    Article  ADS  Google Scholar 

  26. Dakić, B., Vedral, V. & Brukner, Č. Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502–190506 (2010).

    Article  ADS  Google Scholar 

  27. Ferraro, A., Aolita, L., Cavalcanti, D., Cucchietti, F. M. & Acín, A. Almost all quantum states have nonclassical correlations. Phys. Rev. A 81, 052318–052324 (2010).

    Article  ADS  Google Scholar 

  28. Pati, A. K. Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302–014306 (2000).

    Article  ADS  Google Scholar 

  29. Bennett, C. H. et al. Remote state preparation. Phys. Rev. Lett. 87, 077902–077907 (2001).

    Article  ADS  Google Scholar 

  30. Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  31. Groisman, B., Popescu, S. & Winter, A. Quantum, classical, and total amount of correlations in a quantum state. Phys. Rev. A 72, 032317–032328 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  32. Datta, A. Studies on the Role of Entanglement in Mixed-state Quantum Computation. Ph.D. thesis, The Univ. New Mexico (2008).

  33. Horodecki, R. & Horodecki, M. Information-theoretic aspects of inseparability of mixed states. Phys. Rev. A 54, 1838–1843 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  34. Modi, K., Brodutch, A., Cable, H., Paterek, T. & Vedral, V. Quantum discord and other measures of quantum correlation Preprint at (2011).

  35. Chiuri, A., Vallone, G., Paternostro, M. & Mataloni, P. Extremal quantum correlations: Experimental study with two-qubit states. Phys. Rev. A 84, 020304–020308 (2011).

    Article  ADS  Google Scholar 

  36. Luo, S. & Fu, S. Geometric measure of quantum discord. Phys. Rev. A 82, 034302–034306 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  37. Bennett, C., Hayden, P., Leung, D., Shor, P. & Winter, A. Remote preparation of quantum states. Inf. Theory IEEE Trans. 51, 56–74 (2005).

    Article  MathSciNet  Google Scholar 

  38. Werner, R. F. Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989).

    Article  ADS  Google Scholar 

  39. Wootters, W. K. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998).

    Article  ADS  Google Scholar 

  40. Chaves, R. & de Melo, F. Noisy one-way quantum computations: The role of correlations. Phys. Rev. A 84, 022324–022334 (2011).

    Article  ADS  Google Scholar 

  41. Lavoie, J., Kaltenbaek, R., Piani, M. & Resch, K. J. Experimental bound entanglement in a four-photon state. Phys. Rev. Lett. 105, 130501–130505 (2010).

    Article  ADS  Google Scholar 

  42. Amselem, E. & Bourennane, M. Experimental four-qubit bound entanglement. Nature Phys. 5, 748–752 (2009).

    Article  ADS  Google Scholar 

Download references


We acknowledge support from the European Commission, Q-ESSENCE (No 248095), ERC Advanced Senior Grant (QIT4QAD), and the ERA-Net CHIST-ERA project QUASAR, the John Templeton Foundation, Austrian Science Fund (FWF): (SFB-FOCUS) and (Y585-N20) and the doctoral programme CoQuS, and the Air Force Office of Scientific Research, Air Force Material Command, United States Air Force, under grant number FA8655-11-1-3004. The work is supported by the National Research Foundation and Ministry of Education in Singapore.

Author information

Authors and Affiliations



Y.O.L., X.M. and M.R. designed and carried out the experiment, analysed data and wrote the manuscript. B.D., T.P. and V.V. provided the theoretical analysis, analysed data and wrote the manuscript. S.B. designed the experiment, discussed the results and edited the manuscript. S.K. programmed the software. A.Z. supervised the project and edited the manuscript. C.B. supervised the project, provided theoretical analysis and wrote the manuscript. P.W. supervised the project, designed the experiment and wrote the manuscript.

Corresponding authors

Correspondence to Borivoje Dakić or Philip Walther.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 208 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dakić, B., Lipp, Y., Ma, X. et al. Quantum discord as resource for remote state preparation. Nature Phys 8, 666–670 (2012).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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