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.

  • Review Article
  • Published:

Quantum information and computation

Abstract

In information processing, as in physics, our classical world view provides an incomplete approximation to an underlying quantum reality. Quantum effects like interference and entanglement play no direct role in conventional information processing, but they can—in principle now, but probably eventually in practice—be harnessed to break codes, create unbreakable codes, and speed up otherwise intractable computations.

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

Access options

Buy this article

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

Figure 1: Quantum logical operations.
Figure 2: Quantum data compression and error correction.
Figure 3: Quantum information transmission between a sender (Alice) and a receiver (Bob).
Figure 4: Fault-tolerant computation.

Similar content being viewed by others

References

  1. Barenco, A. et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 ( 1995).

    Article  ADS  CAS  Google Scholar 

  2. Zurek, W. Decoherence and the transition from quantum to classical. Phys. Today 44, 36–44 ( 1991).

    Article  Google Scholar 

  3. Preskill, J. Reliable quantum computers. Proc. R. Soc. Lond. A 454 , 385–410 (1998).

    Article  ADS  Google Scholar 

  4. Shor, P. W. in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science 124–133 (IEEE Computer Society Press, Los Alamitos, California, 1994).

    Book  Google Scholar 

  5. Ekert, A. & Jozsa, R. Shor's quantum algorithm for factorising numbers. Rev. Mod. Phys. 68, 733– 753 (1996).

    Article  ADS  CAS  Google Scholar 

  6. Wiesner, S. Simulations of many-body quantum systems by a quantum computer. Preprint quant-ph/9603028 at 〈http://xxx.lanl.gov〉 (1996 ).

  7. Abrams, D. S. & Lloyd, S. Simulations of many-body Fermi systems on a universal quantum computer. Phys. Rev. Lett. 79 , 2586–2589 (1997).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  9. Boyer, M., Brassard, G., Hoyer, P. & Tapp, A. Tight bounds on quantum searching. Fortschr. Phys. 46, 493– 506 (1998).

    Article  Google Scholar 

  10. Ozhigov, Y. Quantum computers cannot speed up iterated applications of a black box. Preprint quant-ph/9712051 at 〈http://xxx.lanl.gov〉 ( 1997).

  11. Terhal, B. M. Quantum Algorithms and Quantum Entanglement. Thesis, Univ. Amsterdam (1999).

    Google Scholar 

  12. Farhi, E., Goldstone, J., Gutmann, S. & Sipser, M. A limit on the speed of quantum computation in determining parity. Phys. Rev. Lett. 81, 5442–5444 (1998).

    Article  ADS  CAS  Google Scholar 

  13. Beals, R., Buhrman, H., Cleve, R., Mosca, M. & de Wolf, R. in Proceedings of the 39th Annual Symposium on the Foundations of Computer Science 352–361 (IEEE Computer Society Press, Los Alamitos, California, 1998).

    Google Scholar 

  14. Jozsa, R. & Schumacher, B. A new proof of the quantum noiseless coding theorem. J. Mod. Opt. 41, 2343– 2349 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  15. Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, 2493–2496 ( 1995).

    Article  ADS  Google Scholar 

  16. Calderbank, A. R. & Shor, P. W. Good quantum error correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996).

    Article  ADS  CAS  Google Scholar 

  17. Steane, A. Multiple particle interference and quantum error correction. Proc. R. Soc. Lond. A 452, 2551–2577 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  18. Knill, E. & Laflamme, R. Theory of quantum error correcting codes. Phys. Rev. A 55, 900– 911 (1997).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  19. Gottesman, D. A class of quantum error-correcting codes saturating the Hamming bound. Phys. Rev. A 54, 1862-1868 (1996 ).

    Article  ADS  MathSciNet  Google Scholar 

  20. Bennett, C. H., DiVincenzo, D. P., Smolin, J. & Wootters, W. K. Mixed state entanglement and quantum error correction. Phys. Rev. A 54, 3824–3851 ( 1996).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  21. Helstrom, C. W. Quantum Detection and Estimation Theory (Academic, New York, 1976).

    MATH  Google Scholar 

  22. Kholevo, A. S. Bounds for the quantity of information transmitted by a quantum communication channel. Problemy Peredachi Informatsii 9, 3–11 (1973); translated in Problems Inf. Transmiss. 9, 177–183 (1973).

    Google Scholar 

  23. Holevo, A. S. Problems in the mathematical theory of quantum communication channels. Rep. Math. Phys. 12, 273–278 (1977).

    Article  ADS  MathSciNet  Google Scholar 

  24. Schumacher, B., Westmoreland, M. & Wootters, W. K. Limitation on the amount of accessible information in a quantum channel. Phys. Rev. Lett. 76, 3452–3455 (1997).

    Article  ADS  Google Scholar 

  25. Holevo, A. S. The capacity of the quantum channel with general signal states. IEEE Trans. Inf. Theory 44, 269–273 (1998).

    Article  MathSciNet  Google Scholar 

  26. Kholevo, A. S. Capacity of a quantum communications channel. Problemy Peredachi Informatsii 15, 3–11 ( 1979); translated in Problems Inf. Transmiss. 15, 247–253 (1979).

    MathSciNet  MATH  Google Scholar 

  27. Sassaki, M., Kato, K., Izutsu, M. & Hirota, O. Quantum channels showing superadditivity in channel capacity. Phys. Rev. A 58, 146–158 (1998).

    Article  ADS  Google Scholar 

  28. Fuchs, C. A. Nonorthogonal quantum states maximize classical information capacity. Phys. Rev. Lett. 79, 1162–1165 (1997).

    Article  ADS  CAS  Google Scholar 

  29. Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895–1898 (1993).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  30. 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).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  31. Bennett, C. H., Shor, P. W., Smolin, J. A. & Thapliyal, A. V. Entanglement enhanced classical capacity of noisy quantum channels. Phys. Rev. Lett. 83, 3081–3084 (1999).

    Article  ADS  CAS  Google Scholar 

  32. Mattle, K., Weinfurter, H., Kwiat, P. G. & Zeilinger, A. Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656–4659 ( 1996).

    Article  ADS  CAS  Google Scholar 

  33. Bouwmeester, D. et al. Experimental quantum teleportation. Nature 390, 575–579 (1997).

    Article  ADS  CAS  Google Scholar 

  34. Boschi, D., Branca, S., De Martini, F., Hardy, L. & Popescu, S. Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 80, 1121– 1124 (1998).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  35. Furusawa, A. et al. Unconditional quantum teleportation. Science 282, 706–709 (1998).

    Article  ADS  CAS  Google Scholar 

  36. Vaidman, L. Teleportation of quantum states. Phys. Rev. A 49, 1473–1476 (1994).

    Article  ADS  CAS  Google Scholar 

  37. Nielsen, M. A., Knill, E. & Laflamme, R. Complete quantum teleportation using nuclear magnetic resonance. Nature 396, 52– 55 (1998).

    Article  ADS  CAS  Google Scholar 

  38. Cleve, R. & Buhrman, H. J. Substituting quantum entanglement for communication. Phys. Rev. A 56, 1201 –1204 (1997).

    Article  ADS  CAS  Google Scholar 

  39. Buhrman, H., Cleve, R. & Wigderson, A. in Proceedings of the 39th Annual ACM Symposium on the Theory of Computing 63–68 (ACM Press, New York, 1998).

    Google Scholar 

  40. Bennett, C. H., Bernstein, H. J., Popescu, S. & Schumacher, B. Concentrating partial entanglement by local operators. Phys. Rev. A 53, 2046–2052 ( 1996).

    Article  ADS  CAS  Google Scholar 

  41. Lo, H.-K. & Popescu, S. Concentrating entanglement by local actions—beyond mean values. Preprint quant-ph/9707038 at 〈http://xxx.lanl.gov〉 (1997).

  42. Vidal, G. Entanglement monotones. Preprint quant-ph/9807077 at 〈http://xxx.lanl.gov〉 (1998).

  43. Linden, N., Popescu, S. & Sudbury, A. Non-local properties of multi-partite density matrices. Phys. Rev. Lett. 83, 243– 247 (1999).

    Article  ADS  CAS  Google Scholar 

  44. Thapliyal, A. V. On multipartite pure-state entanglement. Phys. Rev. A 59, 3336–3342 (1999).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  45. Kempe, J. On multi-particle entanglement and its application to cryptography. Phys. Rev. A 60, 910–916 (1999).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  46. Horodecki, M., Horodecki, P. & Horodecki, R. Mixed state entanglement and distillation: is there a ‘bound’ entanglement in nature? Phys. Rev. Lett. 80, 5239–5242 ( 1998).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  47. Bennett, C. H. et al. Purification of noisy entanglement, and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996).

    Article  ADS  CAS  Google Scholar 

  48. Deutsch, D. et al. Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818–2821 (1996); 80, 2022 (1998) (errata).

    Article  ADS  CAS  Google Scholar 

  49. Bennett, C. H. & Brassard, G. in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India 175–179 (IEEE, New York, 1984).

    Google Scholar 

  50. Mayers, D. Unconditional security in quantum cryptography. Preprint quant-ph/9802025 at 〈http://xxx.lanl.gov〉 (1998).

  51. Lo, H.-K. & Chau, H. F. Unconditional security of quantum key distribution over arbitrarily long distances. Science 283, 2050–2056 (1999).

    Article  ADS  CAS  Google Scholar 

  52. Griffiths, R. B. & Niu, C.-S. Optimal eavesdropping in quantum cryptography. II. Quantum circuit. Phys. Rev. A 56, 1173–1176 (1997).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  53. Biham, E., Boyer, M., Brassard, G., van de Graaf, J. & Mor, T. Security of quantum key distribution against all collective attacks. Phys. Rev. Lett. 78, 2256– 2259 (1997).

    Article  ADS  CAS  Google Scholar 

  54. Mayers, D. Unconditionally secure quantum bit committment is impossible. Phys. Rev. Lett. 78, 3414–3417 (1997).

    Article  ADS  CAS  Google Scholar 

  55. Lo, H.-K. & Chau, H. F. Is quantum bit committment really possible? Phys. Rev. Lett. 78, 3410– 3413 (1997).

    Article  ADS  CAS  Google Scholar 

  56. Muller, A. et al. ‘Plug and Play’ systems for quantum cryptography. Appl. Phys. Lett. 70, 793– 795 (1997).

    Article  ADS  CAS  Google Scholar 

  57. Briegel, H. J., Dür, W., Cirac, J. I. & Zoller, P. Quantum repeaters for communication. Phys. Rev. Lett. 81, 5932–5935 (1998).

    Article  ADS  CAS  Google Scholar 

  58. Dür, W., Briegel, H. J., Cirac, J. I. & Zoller, P. Quantum repeaters based on entanglement purification. Phys. Rev. A 59, 169–181 ( 1999).

    Article  ADS  Google Scholar 

  59. Bennett, C. H. & DiVincenzo, D. P. Quantum computing—towards an engineering era? Nature 377, 389 (1995).

    Article  ADS  CAS  Google Scholar 

  60. van Enk, S. J., Cirac, J. I. & Zoller, P. Ideal quantum communication over noisy channels: a quantum optical implementation. Phys. Rev. Lett. 78, 4293–4296 (1997).

    Article  ADS  CAS  Google Scholar 

  61. van Enk, S. J., Kimble, H. J., Cirac, J. I. & Zoller, P. Quantum communication with dark photons. Phys. Rev. A 59, 2659–2664 (1999).

    Article  ADS  CAS  Google Scholar 

  62. Mabuchi, H., Turchette, Q. A., Chapman, M. S. & Kimble, H. J. Real-time detection of individual atoms falling through a high-finesse optical cavity. Opt. Lett. 21, 1393– 1395 (1996).

    Article  ADS  CAS  Google Scholar 

  63. Haroche, S., Brune, M. & Raimond, J. M. Experiments with single atoms in a cavity: entanglement, Schrodinger's cats and decoherence. Phil. Trans. R. Soc. Lond. A 355, 2367–2380 ( 1997).

    Article  ADS  CAS  Google Scholar 

  64. Turchette, Q. A. et al. Deterministic entanglement of two ions. Phys. Rev. Lett. 81, 3631–3634 ( 1998).

    Article  ADS  CAS  Google Scholar 

  65. Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M. & Wineland, D. J. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714–4717 (1995).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  66. DiVincenzo, D. P. & Loss, D. Quantum information is physical. Superlatt. Microstruct. 23, 419–432 (1998).

    Article  ADS  CAS  Google Scholar 

  67. Cirac, J. I. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091– 4094 (1995).

    Article  ADS  CAS  Google Scholar 

  68. Lloyd, S. A potentially realizable quantum computer. Science 261, 1569–1571 (1993).

    Article  ADS  CAS  Google Scholar 

  69. Lloyd, S. Envisioning a quantum supercomputer. Science 263, 695 (1994).

    Article  ADS  CAS  Google Scholar 

  70. Cory, D. G., Fahmy, A. F. & Havel, T. F. Ensemble quantum computing by nuclear magnetic resonance spectroscopy. Proc. Natl. Acad. Sci. USA 94, 1634–1639 (1997).

    Article  ADS  CAS  Google Scholar 

  71. Gershenfeld, N. A. & Chuang, I. L. Bulk spin resonance quantum computation. Science 275, 350– 356 (1997).

    Article  MathSciNet  CAS  Google Scholar 

  72. Cory, D. G., Price, M. D. & Havel, T. F. Nuclear magnetic resonance spectroscopy: an experimentally accessible paradigm for quantum computing. Physica D 120, 82–101 (1998).

    Article  ADS  CAS  Google Scholar 

  73. Chuang, I. L., Vandersypen, L. M. K., Xinlan ZhouLeung, D. W. & Lloyd, S. Experimental realization of a quantum algorithm. Nature 393, 143–146 (1998).

    Article  ADS  CAS  Google Scholar 

  74. Chuang, I. L., Gershenfeld, N. & Kubinec, M. Experimental implementation of fast quantum searching. Phys. Rev. Lett. 80, 3408– 3411 (1998).

    Article  ADS  CAS  Google Scholar 

  75. Laflamme, R., Knille, E., Zurek, W. H., Catasti, P. & Mariappan, S. V. S. NMR Greenberger Horne Zeilinger states. Phil. Trans. R. Soc. Lond. A 356, 1941– 1948 (1998).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  76. Cory, D. G. et al. Experimental quantum error correction. Phys. Rev. Lett. 81, 2152–2155 ( 1998).

    Article  ADS  CAS  Google Scholar 

  77. Jones, J. A. & Mosca, M. Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer. J. Chem. Phys. 109, 1648–1653 ( 1998).

    Article  ADS  CAS  Google Scholar 

  78. Jones, J. A. & Mosca, M. Approximate quantum counting on an NMR ensemble quantum computer. Phys. Rev. Lett. 83, 1050–1053 (1999).

    Article  ADS  CAS  Google Scholar 

  79. Linden, N., Barjat, H. & Freeman, R. An implementation of the Deutsch Jozsa algorithm on a three qubit NMR quantum computer. Chem. Phys. Lett. 296, 61–67 (1998).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported by the US Army Research office.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Charles H. Bennett.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bennett, C., DiVincenzo, D. Quantum information and computation. Nature 404, 247–255 (2000). https://doi.org/10.1038/35005001

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/35005001

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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