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Preparing tunable Bell-diagonal states on a quantum computer

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Abstract

The class of two-qubit Bell-diagonal states has been the workhorse for developing understanding about the geometry, dynamics, and applications of quantum resources. In this article, we present a quantum circuit for preparing Bell-diagonal states on a quantum computer in a tunable way. We implement this quantum circuit using the IBM Q 5 Yorktown quantum computer, and as an application example, we measure the non-local, steering, entanglement, and discord quantum correlations and non-local quantum coherence of Werner states.

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References

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

    Article  ADS  Google Scholar 

  2. Bell, J.S.: On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447 (1966)

    Article  ADS  MathSciNet  Google Scholar 

  3. Schrödinger, E.: Discussion of probability relations between separated systems. Math. Proc. Camb. Philos. Soc. 31, 555 (1935)

    Article  ADS  Google Scholar 

  4. 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 

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

    Article  ADS  Google Scholar 

  6. Shi, H.-L., Liu, S.-Y., Wang, X.-H., Yang, W.-L., Yang, Z.-Y., Fan, H.: Coherence depletion in the Grover quantum search algorithm. Phys. Rev. A 95, 032307 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  7. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)

    Article  ADS  Google Scholar 

  8. Branciard, C., Cavalcanti, E.G., Walborn, S.P., Scarani, V., Wiseman, H.M.: One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering. Phys. Rev. A 85, 010301 (2012)

    Article  ADS  Google Scholar 

  9. Popescu, S.: Bell’s inequalities versus teleportation: What is nonlocality? Phys. Rev. Lett. 72, 797 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  10. Streltsov, A., Kampermann, H., Bruß, D.: In: Fanchini F.F., Soares-Pinto D.O., Adesso G. (eds.) Lectures on General Quantum Correlations and Their Applications, pp. 217–230. Springer (2017)

  11. Brito, S.G.A., Amaral, B., Chaves, R.: Noncontextual wirings. Phys. Rev. A 97, 022111 (2018)

    Article  ADS  Google Scholar 

  12. Gallego, R., Aolita, L.: The resource theory of steering. Phys. Rev. X 5, 041008 (2015)

    MATH  Google Scholar 

  13. Vedral, V., Plenio, M.B., Rippin, M.A., Knight, P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275 (1997)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Gharibian, S.: Strong NP-hardness of the quantum separability problem. Quantum Inf. Comp. 10, 343 (2010)

    MathSciNet  MATH  Google Scholar 

  16. Huang, Y.: Computing quantum discord is NP-complete. New J. Phys. 16, 033027 (2014)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  18. Lang, M.D., Caves, C.M.: Quantum discord and the geometry of Bell-diagonal states. Phys. Rev. Lett. 105, 150501 (2010)

    Article  ADS  Google Scholar 

  19. Quan, Q., Zhu, H., Liu, S.-Y., Fei, S.-M., Fan, H., Yang, W.-L.: Steering Bell-diagonal states. Sci. Rep. 6, 22025 (2016)

    Article  ADS  Google Scholar 

  20. Roszak, K., Cywiński, Ł.: The relation between the quantum discord and quantum teleportation: the physical interpretation of the transition point between different quantum discord decay regimes. EPL 112, 10002 (2015)

    Article  ADS  Google Scholar 

  21. Meng, Q., Yan-Biao, L., Xiao, W., Zhong, B.: The decoherence of quantum entanglement and teleportation in Bell-diagonal states. Chin. Phys. C 36, 307 (2012)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Wang, Y.-K., Ma, T., Fan, H., Fei, S.-M., Wang, Z.-X.: Super-quantum correlation and geometry for Bell-diagonal states with weak measurements. Quantum Inf. Proc. 13, 283 (2014)

    Article  ADS  Google Scholar 

  24. Singh, H., Arvind, Dorai, K.: Experimentally freezing quantum discord in a dephasing environment using dynamical decoupling. EPL 118, 50001 (2017)

    Article  ADS  Google Scholar 

  25. Maziero, J., Céleri, L.C., Serra, R.M., Vedral, V.: Classical and quantum correlations under decoherence. Phys. Rev. A 80, 044102 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  26. Céleri, L.C., Maziero, J.: In: Fanchini F.F., Soares-Pinto D.O., Adesso G. (eds.) Lectures on General Quantum Correlations and their Applications, pp. 309–337. Springer (2017)

  27. Castro, C.S., Duarte, O.S., Pires, D.P., Soares-Pinto, D.O., Reis, M.S.: Thermal entanglement and teleportation in a dipolar interacting system. Phys. Lett. A 380, 1571 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  28. Paula, F.M., Saguia, A., de Oliveira, T.R., Sarandy, M.S.: Overcoming ambiguities in classical and quantum correlation measures. EPL 108, 10003 (2014)

    Article  ADS  Google Scholar 

  29. Luo, S., Zhang, Q.: Observable correlations in two-qubit states. J. Stat. Phys. 136, 165 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  30. Hou, J.-X., Su, Y.-L., Liu, S.-Y., Wang, X.-H., Yang, W.-L.: Geometric structure of quantum resources for Bell-diagonal states. Quantum Inf. Process. 17, 184 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  31. Han, W., Jiang, K.-X., Zhang, Y.-J., Xia, Y.-J.: Quantum speed limits for Bell-diagonal states. Chin. Phys. B 24, 120304 (2015)

    Article  ADS  Google Scholar 

  32. Bromley, T.R., Cianciaruso, M., Adesso, G.: Frozen quantum coherence. Phys. Rev. Lett. 114, 210401 (2015)

    Article  ADS  Google Scholar 

  33. Bromley, T.R., Cianciaruso, M., Franco, R.L., Adesso, G.: Unifying approach to the quantification of bipartite correlations by Bures distance. J. Phys. A Math. Theor. 47, 405302 (2014)

    Article  MathSciNet  Google Scholar 

  34. Du, M.-M., Wang, D., Ye, L.: The dynamic behaviors of complementary correlations under decoherence channels. Sci. Rep. 7, 40934 (2017)

    Article  ADS  Google Scholar 

  35. 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 

  36. 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 

  37. Aguilar, G.H., Farías, O.J., Maziero, J., Serra, R.M., Ribeiro, P.H.S., Walborn, S.P.: Experimental estimate of a classicality witness via a single measurement. Phys. Rev. Lett. 108, 063601 (2012)

    Article  ADS  Google Scholar 

  38. Liu, T.-J., Wang, C.-Y., Li, J., Wang, Q.: Experimental preparation of an arbitrary tunable Werner state. EPL 119, 14002 (2017)

    Article  ADS  Google Scholar 

  39. IBM Quantum Experience. http://www.research.ibm.com/ibm-q

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

    Article  ADS  MathSciNet  Google Scholar 

  41. Li, Z.-N., Jin, J.-S., Yu, C.-S.: Probing Bell diagonal state without disturbing its correlations. Commun. Theor. Phys. 58, 47 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  42. Li, J., Wang, C.-Y., Liu, T.-J., Wang, Q.: Experimental verification of steerability via geometric Bell-like inequalities. Phys. Rev. A 97, 032107 (2018)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  44. Maziero, J.: Computing partial traces and reduced density matrices. Int. J. Mod. Phys. C 28, 1750005 (2016)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  46. Pozzobom, M.B., Maziero, J.: Environment-induced quantum coherence spreading of a qubit. Ann. Phys. 377, 243 (2017)

    Article  ADS  Google Scholar 

  47. Radhakrishnan, C., Parthasarathy, M., Jambulingam, S., Byrnes, T.: Distribution of quantum coherence in multipartite systems. Phys. Rev. Lett. 116, 150504 (2016)

    Article  ADS  Google Scholar 

  48. Vidal, G., Werner, R.F.: A computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  49. Maziero, J.: Computing partial transposes and related entanglement functions. Braz. J. Phys. 46, 605 (2016)

    ADS  Google Scholar 

  50. Costa, A.C.S., Angelo, R.M.: Quantification of Einstein–Podolski–Rosen steering for two-qubit states. Phys. Rev. A 93, 020103 (2016)

    Article  ADS  Google Scholar 

  51. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)

    Article  ADS  Google Scholar 

  52. Horodecki, R., Horodecki, P., Horodecki, M.: Violating Bell inequality by mixed spin-12 states: necessary and sufficient condition. Phys. Lett. A 200, 340 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  53. Cavalcanti, E.G., Foster, C.J., Fuwa, M., Wiseman, H.M.: Analog of the Clauser–Horne–Shimony–Holt inequality for steering. J. Opt. Soc. Am. B 32, A74 (2015)

    Article  ADS  Google Scholar 

  54. Mandarino, A., Bina, M., Porto, C., Cialdi, S., Olivares, S., Paris, M.G.A.: Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous variable systems. Phys. Rev. A 93, 062118 (2016)

    Article  ADS  Google Scholar 

  55. Soares-Pinto, D.O., Moussa, M.H.Y., Maziero, J., deAzevedo, E.R., Bonagamba, T.J., Serra, R.M., Céleri, L.C.: Equivalence between Redfield- and Master-equation approaches for a time-dependent quantum system and coherence control. Phys. Rev. A 83, 062336 (2011)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the Brazilian National Institute for the Science and Technology of Quantum Information (INCT-IQ), process 465469/2014-0, and by the Coordination for the Improvement of Higher Education Personnel (CAPES).

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Correspondence to Jonas Maziero.

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Pozzobom, M.B., Maziero, J. Preparing tunable Bell-diagonal states on a quantum computer. Quantum Inf Process 18, 142 (2019). https://doi.org/10.1007/s11128-019-2264-z

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