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Quantifying quantum information resources: a numerical study

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Abstract

Quantum systems present correlations, which cannot be offered by classical objects. These distinctive correlations are not only considered as fundamental features of quantum mechanics, but more importantly, they are regarded as critical resources for different quantum information tasks. For example, quantum entanglement has been established as the key resource for quantum communication, and quantum discord has been suggested as the resource in deterministic quantum computation with one qubit (DQC1). However, quantification of these resources is very difficult, especially for many-body situations. Here, we introduce a unified numerical method to quantify these resources in general multiqubit states and use it to investigate the robustness of quantum discord in multiqubit permutation-invariant states. Our method paves the way to quantitatively investigate the relation between the potential of quantum technologies and quantum resources, particularly, that between quantum computation and quantum correlations.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Barrett J, Hardy L, Kent A. No signaling and quantum key distribution. Phys Rev Lett, 2005, 95: 010503

    Article  Google Scholar 

  3. Acin A, Brunner N, Gisin N, et al. Device-independent security of quantum cryptography against collective attacks. Phys Rev Lett, 2007, 98: 230501

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Lanyon B P, Barbieri M, Almeida M P, et al. Experimental quantum computing without entanglement. Phys Rev Lett, 2008, 101: 200501

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  7. Bell J S. On the problem of hidden variables in quantum mechanics. Rev Mod Phys, 1966, 38: 447–452

    Article  MathSciNet  MATH  Google Scholar 

  8. Kochen S, Specker E P. The problem of hidden variables in quantum mechanics. J Math Mech, 1967, 17: 59–87

    MathSciNet  MATH  Google Scholar 

  9. Howard M, Wallman J, Veitch V, et al. Contextuality supplies the ‘magic’ for quantum computation. Nature, 2014, 510: 351–355

    Google Scholar 

  10. Raussendorf R, Browne D E, Delfosse N, et al. Contextuality and Wigner function negativity in qubit quantum computation. arXiv:1511.08506

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

    Article  Google Scholar 

  12. Bennett C H, Bernstein H J, Popescu S, et al. Concentrating partial entanglement by local operations. Phys Rev A, 1996, 53: 2046–2052

    Article  Google Scholar 

  13. Bennett C H, Di Vincenzo D P, Smolin J A, et al. Mixed-state entanglement and quantum error correction. Phys Rev A, 1996, 54: 3824–3851

    Article  MathSciNet  Google Scholar 

  14. Bennett C H, Brassard G, Popescu S, et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys Rev Lett, 1996, 76: 722–725

    Article  Google Scholar 

  15. Coffman V, Kundu J, Wootters W K. Distributed entanglement. Phys Rev A, 2000, 61: 052306

    Article  Google Scholar 

  16. Henderson L, Vedral V. Classical, quantum and total correlations. J Phys A: Math Gen, 2001, 34: 6899–6905

    Article  MathSciNet  MATH  Google Scholar 

  17. Okrasa M, Walczak Z. Quantum discord and multipartite correlations. Europhys Lett, 2011, 96: 60003

    Article  Google Scholar 

  18. Chakrabarty I, Agrawal P, Pati A K. Quantum dissension: generalizing quantum discord for three-qubit states. Eur Phys J D, 2011, 65: 605–612

    Article  Google Scholar 

  19. Modi K, Paterek T, Son W, et al. Unified view of quantum and classical correlations. Phys Rev Lett, 2010, 104: 080501

    Article  MathSciNet  Google Scholar 

  20. Grudka A, Horodecki K, Horodecki M, et al. Quantifying contextuality. Phys Rev Lett, 2014, 112: 120401

    Article  Google Scholar 

  21. Gour G, Müller M P, Narasimhachar V, et al. The resource theory of informational nonequilibrium in thermodynamics. Phys Rep, 2015, 583: 1–58

    Article  MathSciNet  MATH  Google Scholar 

  22. Hukushima K, Nemoto K. Exchange Monte Carlo method and application to spin glass simulations. J Phys Soc Jpn, 1996, 65: 1604–1608

    Article  Google Scholar 

  23. Marinari E, Parisi G. Simulated tempering: a new Monte Carlo scheme. Europhys Lett, 1992, 19: 451–458

    Article  Google Scholar 

  24. Geyer C J, Thompson E A. Constrained Monte Carlo maximum likelihood for dependent data. J R Stat Soc Ser B, 1992, 54: 657–699

    MathSciNet  Google Scholar 

  25. Young A P. Spin Glasses and Random Fields. Singapore River Edge: World Scientific, 1998

    Google Scholar 

  26. Vedral V, Plenio M B, Rippin M A, et al. Quantifying entanglement. Phys Rev Lett, 1997, 78: 2275–2279

    Article  MathSciNet  MATH  Google Scholar 

  27. Marinari E, Parisi G, Ruiz-Lorenzo J J. Phase structure of the three-dimensional edwards-anderson spin glass. Phys Rev B, 1998, 58: 14852–14863

    Article  Google Scholar 

  28. Sugita Y, Kitao A, Okamoto Y. Multidimensional replica-exchange method for free-energy calculations. J Chem Phys, 2000, 113: 6042–6051

    Article  Google Scholar 

  29. Neirotti J P, Calvo F, Freeman D L, et al. Phase changes in 38-atom Lennard-Jones clusters. I. A parallel tempering study in the canonical ensemble. J Chem Phys, 2000, 112: 10340–10349

    Google Scholar 

  30. Cao K, Zhou Z W, Guo G C, et al. Efficient numerical method to calculate the three-tangle of mixed states. Phys Rev A, 2010, 81: 034302

    Article  Google Scholar 

  31. Sasaki G H, Hajek B. The time-complexity of maximum matching by simulated annealing. J ACM, 1988, 35: 387–403

    Article  MathSciNet  MATH  Google Scholar 

  32. Kirkpatrick S, Gelatt C D, Vecchi M P. Optimization by simulated annealing. Science, 1983, 220: 671–680

    Article  MathSciNet  MATH  Google Scholar 

  33. Bertsimas D, Tsitsiklis J. Simulated annealing. Stat Sci, 1993, 8: 10–15

    Article  MATH  Google Scholar 

  34. Wang W, Machta J, Katzgraber H G. Comparing Monte Carlo methods for finding ground states of ising spin glasses: population annealing, simulated annealing, and parallel tempering. Phys Rev E, 2015, 92: 013303

    Article  MathSciNet  Google Scholar 

  35. Moreno J J, Katzgraber H G, Hartmann A K. Finding low-temperature states with parallel tempering, simulated annealing and simple Monte Carlo. Int J Mod Phys C, 2003, 14: 285–302

    Article  Google Scholar 

  36. Earl D J, Deem M W. Parallel tempering: theory, applications, and new perspectives. Phys Chem Chem Phys, 2005, 7: 3910–3916

    Article  Google Scholar 

  37. Wei T C. Relative entropy of entanglement for multipartite mixed states: permutation-invariant states and dür states. Phys Rev A, 2008, 78: 012327

    Article  Google Scholar 

  38. Parashar P, Rana S. Entanglement and discord of the superposition of greenberger-horne-zeilinger states. Phys Rev A, 2011, 83: 032301

    Article  Google Scholar 

  39. Yu T, Eberly J H. Sudden death of entanglement. Science, 2009, 323: 598–601

    Article  MathSciNet  MATH  Google Scholar 

  40. Werlang T, Souza S, Fanchini F F, et al. Robustness of quantum discord to sudden death. Phys Rev A, 2009, 80: 024103

    Article  Google Scholar 

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Acknowledgments

Lixin HE acknowledges the support from Chinese National Fundamental Research Program (Grant No. 2011CB921200), National Natural Science Funds for Distinguished Young Scholars, and the Fundamental Research Funds for the Central Universities (Grant No. WK2470000006).

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Authors and Affiliations

  1. Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei, 230026, China

    Zhen Wang & Lixin He

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  1. Zhen Wang
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  2. Lixin He
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Correspondence to Lixin He.

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Wang, Z., He, L. Quantifying quantum information resources: a numerical study. Sci. China Inf. Sci. 60, 052501 (2017). https://doi.org/10.1007/s11432-016-9006-6

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  • DOI: https://doi.org/10.1007/s11432-016-9006-6

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