Skip to main content
SpringerLink
Log in

Experimental estimation of discord in an antiferromagnetic Heisenberg compound \(\hbox {Cu}(\hbox {NO}_{3})_{2}\cdot 2.5\,\hbox {H}_{2}\hbox {O}\)

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Temperature-dependent static magnetic susceptibility and heat capacity data were employed to quantify quantum discord in copper nitrate \((\hbox {CN, Cu}(\hbox {NO}_{3})_{2}\cdot 2.5\, \hbox {H}_{2}\hbox {O})\) which is a spin 1/2 antiferromagnetic Heisenberg system. With the help of existing theoretical formulations, quantum discord, mutual information, and purely classical correlation were estimated as a function of temperature using the experimental data. The experimentally quantified correlations estimated from susceptibility and heat capacity data are consistent with each other, and they exhibit a good match with theoretical predictions. Violation of Bell’s inequality was also checked using the static magnetic susceptibility as well as heat capacity data. Quantum discord estimated from magnetic susceptibility as well as heat capacity data is found to be present in the thermal states of the system even when the system is in a separable state.

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
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. 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 

  3. Vedral, V.: Quantifying entanglement in macroscopic systems. Nature (London) 453, 1004 (2008). For a review, see Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglements in many body systems. Rev. Mod. Phys. 80, 517 (2008)

  4. Wieśniak, M., Vedral, V., Brukner, Č.: Heat capacity as an indicator of entanglement. Phys. Rev. B 78, 064108 (2008)

    Article  ADS  Google Scholar 

  5. Wieśniak, M., Vedral, V., Brukner, Č.: Magnetic susceptibility as a macroscopic entanglement witness. New J. Phys. 7, 258 (2005)

    Article  ADS  Google Scholar 

  6. Bose, S.: Quantum communication through an unmodulated spin chain. Phys. Rev. Lett. 91, 207901 (2003)

    Article  ADS  Google Scholar 

  7. Arnesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)

    Article  ADS  Google Scholar 

  8. Bose, I., Tribedi, A.: Thermal entanglement properties of small spin clusters. Phys. Rev. A 72, 022314 (2005)

    Article  ADS  Google Scholar 

  9. Brukner, Č., Vedral, V., Zeilinger, A.: Crucial role of quantum entanglement in bulk properties of solids. Phys. Rev. A 73, 012110 (2006)

    Article  ADS  Google Scholar 

  10. Souza, A.M., Soares-Pinto, D.O., Sarthour, R.S., Oliveira, I.S., Reis, M.S., Brandão, P., dos Santos, A.M.: Entanglement and Bell’s inequality violation above room temperature in metal carboxylates. Phys. Rev. B 79, 054408 (2009)

    Article  ADS  Google Scholar 

  11. Rappoport, T.G., Ghivelder, L., Fernandes, J.C., Guimaraes, R.B., Continentino, M.A.: Experimental observation of quantum entanglement in low-dimensional spin systems. Phys. Rev. B 75, 054422 (2007)

    Article  ADS  Google Scholar 

  12. Souza, A.M., Reis, M.S., Soares-Pinto, D.O., Oliveira, I.S., Sarthour, R.S.: Experimental determination of thermal entanglement in spin clusters using magnetic susceptibility measurements. Phys. Rev. B 77, 104402 (2008)

    Article  ADS  Google Scholar 

  13. Das, D., Singh, H., Chakraborty, T., Gopal, R.K., Mitra, C.: Experimental detection of quantum information sharing and its quantification in quantum spin systems. New J. Phys. 15, 013047 (2013)

    Article  ADS  Google Scholar 

  14. Singh, H., Chakraborty, T., Das, D., Jeevan, H.S., Tokiwa, Y., Gegenwart, P., Mitra, C.: Experimental quantification of entanglement through heat capacity. New J. Phys. 15, 113001 (2013)

    Article  ADS  Google Scholar 

  15. Bell, J.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964)

    Google Scholar 

  16. Meyer, D.A.: Sophisticated quantum search without quantum entanglement. Phys. Rev. Lett. 85, 2014 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2002)

    Article  ADS  Google Scholar 

  20. Braunstein, S.L., Caves, C.M., Jozsa, R., Linden, N., Popescu, S., Schack, R.: Separability of very noisy mixed states and implications for NMR quantum computing. Phys. Rev. Lett. 83, 1054 (1999)

    Article  ADS  Google Scholar 

  21. Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shor, P.W., Smolin, J.A., Wootters, W.K.: Quantum nonlocality without entanglement. Phys. Rev. A 59, 1070 (1999)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. DiVincenzo, D., Horodecki, M., Leung, D.W., Smolin, J.A., Terhal, B.M.: Locking classical correlations in quantum states. Phys. Rev. Lett. 92, 067902 (2004)

    Article  ADS  Google Scholar 

  25. Ferraro, A., Aolita, L., Cavalcanti, D., Cucchietti, F.M., Acín, A.: Almost all quantum states have non-classical correlations. Phys. Rev. A 81, 052318 (2010)

    Article  ADS  Google Scholar 

  26. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  27. Dillenschneider, R.: Quantum discord and quantum phase transition in spin chains. Phys. Rev. B 78, 224413 (2008)

    Article  ADS  Google Scholar 

  28. Auccaise, R., Céleri, L.C., Soares-Pinto, D.O., deAzevedo, E.R., Maziero, J., Souza, A.M., Bonagamba, T.J., Sarthour, R.S., Oliveira, I.S., Serra, R.M.: Environment-induced sudden transition in quantum discord dynamics. Phys. Rev. Lett. 107, 140403 (2011)

    Article  ADS  Google Scholar 

  29. Auccaise, R., Maziero, J., Céleri, L.C., Soares-Pinto, D.O., deAzevedo, E.R., Bonagamba, T.J., Sarthour, R.S., Oliveira, I.S., Serra, R.M.: Experimentally witnessing the quantumness of correlations. Phys. Rev. Lett. 107, 070501 (2011)

    Article  ADS  Google Scholar 

  30. Maziero, J., Auccaise, R., Céleri, L.C., Soares-Pinto, D.O., deAzevedo, E.R., Bonagamba, T.J., Sarthour, R.S., Oliveira, I.S., Serra, R.M.: Quantum discord in nuclear magnetic resonance system at room temperature. Braz. J. Phys. 43, 86 (2013)

    Article  ADS  Google Scholar 

  31. Werlang, T., Trippe, C., Ribeiro, G.A.P., Rigolin, G.: Quantum correlations in spin chains at finite temperatures and quantum phase transitions. Phys. Rev. Lett. 105, 095702 (2010)

    Article  ADS  Google Scholar 

  32. Werlang, T., Rigolin, G.: Thermal and magnetic quantum discord in Heisenberg models. Phys. Rev. A 81, 044101 (2010)

    Article  ADS  Google Scholar 

  33. Pal, A.K., Bose, I.: Quantum discord in the ground and thermal states of spin clusters. J. Phys. B 44, 045101 (2011)

    Article  ADS  Google Scholar 

  34. Maziero, J., Guzman, H.C., Celeri, L.C., Sarandy, M.S., Serra, R.M.: Quantum and classical thermal correlations in the XY spin-1/2 chain. Phys. Rev. A 82, 012106 (2010)

    Article  ADS  Google Scholar 

  35. Modi, K., Brodutch, A., Cabb, H., Paterek, T., Vedral, V.: quant-ph/1112.6238v1

  36. Bonner, J.C., Friedberg, S.A., Kobayashi, H., Meier, D.L., Blote, H.W.J.: Alternating linear-chain antiferromagnetism in copper nitrate \(\text{ Cu }(\text{ NO }_{3})_{2} \cdot 2.5\, \text{ H }_{2}\text{ O }\). Phys. Rev. B 27, 1 (1983)

    Article  Google Scholar 

  37. Xu, G., Broholm, C., Reich, D.H., Adams, M.A.: Triplet waves in a quantum spin liquid. Phys. Rev. Lett. 84, 4465 (2000)

    Article  ADS  Google Scholar 

  38. Berger, L., Friedberg, S.A., Schriemf, J.T.: Magnetic susceptibility of \(\text{ Cu }(\text{ NO }_{3})_{2} \cdot 2.5\, \text{ H }_{2}\text{ O }\) at low temperature*. Phys. Rev. 132, 1057 (1963)

    Article  ADS  Google Scholar 

  39. Yurishchev, M.A.: Quantum discord in spin-cluster materials. Phys. Rev. B 84, 024418 (2013)

    Article  ADS  Google Scholar 

  40. Bleaney, B., Bowers, K.D.: Anomalous paramagnetism in copper acetate. Proc. R. Soc. A 214, 451 (1952)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Brukner, Č., Żukowski, M., Pan, J.W., Zeilinger, A.: Bell’s inequalities and quantum communications complexity. Phys. Rev. Lett. 92, 127901 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  43. Acin, A., Gisin, N., Masanes, L.: From Bell’s theorem to secure quantum key distribution. Phys. Rev. Lett. 97, 120405 (2006)

    Article  ADS  Google Scholar 

  44. Friedberg, S.A., Raquet, C.A.: The heat capacity of \(\text{ Cu }(\text{ NO }_{3})_{2} \cdot 2.5\, \text{ H }_{2}\text{ O }\) at low temperature*. J. App. Phys. 39, 2 (1968)

    Article  Google Scholar 

  45. Wang, X., Zanardi, P.: Quantum entanglement and Bell inequalities in Heisenberg spin chains. Phys. Lett. A 301, 1–6 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

We would like to thank Ministry of Human Resource and Development (MHRD), Govt. of India, for funding.

Author information

Authors and Affiliations

  1. Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur, Nadia, 741246, West Bengal, India

    H. Singh, T. Chakraborty, P. K. Panigrahi & C. Mitra

  2. Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400005, India

    H. Singh

Authors
  1. H. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. K. Panigrahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. Mitra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Mitra.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, H., Chakraborty, T., Panigrahi, P.K. et al. Experimental estimation of discord in an antiferromagnetic Heisenberg compound \(\hbox {Cu}(\hbox {NO}_{3})_{2}\cdot 2.5\,\hbox {H}_{2}\hbox {O}\) . Quantum Inf Process 14, 951–961 (2015). https://doi.org/10.1007/s11128-014-0913-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-014-0913-9

Keywords

Search

Navigation