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Quantum-Enhanced Measurements: Beating the Standard Quantum Limit

Open access
Giovannetti, Vittorio, Lloyd, Seth, Maccone, Lorenzo·2004·Science

Abstract

Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurement. Conventional measurement techniques typically fail to reach these limits. Conventional bounds to the precision of measurements such as the shot noise limit or the standard quantum limit are not as fundamental as the Heisenberg limits and can be beaten using quantum strategies that employ “quantum tricks” such as squeezing and entanglement.

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Show all 10 references

Research works printed but not linked: 72

  1. 10.1103/PhysRev.34.163 · DOI · Paper page
  2. 10.1103/RevModPhys.52.341 · DOI · Paper page
  3. 10.1103/PhysRevLett.75.3422 · doi:10.1103/physrevlett.75.3422
  4. 10.1103/PhysRevA.28.2065 · DOI
  5. V. B. Braginsky F. Ya Khalili Quantum Measurements (Cambridge Univ. Press Cambridge 1992). · DOI · Paper page
  6. 10.1103/PhysRevA.33.4033 · DOI · Paper page
  7. C. W. Helstrom Quantum Detection and Estimation Theory (Academic Press New York 1976).
  8. 10.1070/PU1975v017n05ABEH004362 · DOI · Paper page
  9. 10.1140/epjd/e2003-00003-3 · DOI
  10. 10.1103/PhysRevLett.75.2944 · DOI · Paper page
  11. R. S. Bondurant, J. H. Shapiro, Phys. Rev. D30, 2548 (1984).
  12. 10.1103/PhysRevLett.59.278 · DOI · Paper page
  13. 10.1103/PhysRevLett.71.1355 · DOI · Paper page
  14. L. Mandelstam, I. G. Tamm, J. Phys. USSR9, 249 (1945).
  15. 10.1103/PhysRevA.54.R4649 · DOI · Paper page
  16. 10.1103/PhysRevA.55.2598 · DOI · Paper page
  17. 10.1007/BF01135861 · DOI
  18. P. Kok, S. L. Braunstein, J. P. Dowling, J. Opt. B Quantum Semiclass. Opt.6, 5811 (2004).
  19. 10.1103/PhysRevLett.91.047902 · DOI
  20. 10.1103/PhysRevA.67.062307 · DOI
  21. 10.1103/PhysRevLett.87.270404 · DOI · Paper page
  22. 10.1007/BF01872783 · DOI
  23. 10.1103/PhysRevLett.85.2733 · DOI · Paper page
  24. 10.1103/PhysRevLett.87.013602 · DOI · Paper page
  25. 10.1007/BF00620308 · DOI · Paper page
  26. 10.1103/PhysRevLett.82.2868 · DOI
  27. 10.1038/35086525 · DOI · Paper page
  28. 10.1103/PhysRevLett.87.117902 · DOI
  29. 10.1103/PhysRevLett.85.2010 · DOI · Paper page
  30. 10.1103/PhysRevA.45.3126 · DOI · Paper page
  31. 10.1103/RevModPhys.71.1539 · DOI · Paper page
  32. 10.1088/1464-4266/4/3/372 · DOI · Paper page
  33. 10.1103/PhysRevA.52.R3429 · DOI · Paper page
  34. 10.1103/PhysRevLett.89.113601 · DOI · Paper page
  35. 10.1103/PhysRevA.70.013802 · DOI · Paper page
  36. 10.1364/OL.25.000076 · DOI
  37. 10.1103/PhysRevLett.88.203601 · DOI · Paper page
  38. 10.1103/PhysRevLett.85.3789 · DOI
  39. 10.1103/PhysRevLett.87.167901 · DOI
  40. 10.1103/PhysRevLett.87.257903 · DOI
  41. 10.1103/PhysRevLett.93.180503 · DOI
  42. 10.1103/PhysRevLett.83.432 · DOI
  43. 10.1088/0022-3735/11/7/030 · DOI
  44. 10.1103/PhysRevLett.51.719 · DOI
  45. 10.1103/PhysRevLett.54.2465 · DOI
  46. 10.1103/PhysRevLett.60.385 · DOI
  47. 10.1103/PhysRevLett.45.75 · DOI · Paper page
  48. W. G. Unruh, in Quantum Optics, Experimental Gravitation and Measurement Theory, P. Meystre, M. O. Scully, Eds. (Plenum, New York, 1983), p. 647.
  49. 10.1209/0295-5075/13/4/003 · DOI · Paper page
  50. 10.1103/PhysRevA.47.3173 · DOI · Paper page
  51. 10.1103/RevModPhys.68.755 · DOI · Paper page
  52. 10.1038/nature01773 · DOI · Paper page
  53. 10.1126/science.1094419 · DOI · Paper page
  54. 10.1103/PhysRevA.51.2459 · DOI
  55. 10.1103/PhysRevLett.80.688 · DOI · Paper page
  56. 10.1103/PhysRevLett.83.3174 · DOI · Paper page
  57. G. M. D'Ariano, M. Sacchi, R. Seno, Nuovo Cimento B114, 775 (1999).
  58. 10.1103/PhysRevA.32.2287 · DOI · Paper page
  59. 10.1038/22275 · DOI · Paper page
  60. 10.1038/25059 · DOI · Paper page
  61. 10.1016/0375-9601(90)90442-Q · doi:10.1016/0375-9601(90)90442-q
  62. 10.1103/PhysRevD.64.042006 · DOI · Paper page
  63. 10.1103/RevModPhys.29.255 · DOI · Paper page
  64. B. S. De Witt in Gravitation: An Introduction to Current Research L. Witten Ed. (Wiley New York 1962).
  65. S. Lloyd, Nature406, 1047 (2004).
  66. C. Callender N. Huggett Eds. Physics Meets Philosophy at the Planck Scale: Contemporary Theories in Quantum Gravity (Cambridge Univ. Press Cambridge 2001). · DOI · Paper page
  67. J. D. Bekenstein, Phys. Rev. D23, 287 (1981).
  68. 10.1063/1.531249 · DOI · Paper page
  69. 10.1103/RevModPhys.74.825 · DOI · Paper page
  70. 10.1103/PhysRevLett.86.2946 · DOI
  71. 10.1103/PhysRevLett.91.041302 · DOI
  72. 10.1038/351111a0 · DOI · Paper page

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Metadata

Authors
Giovannetti, V., Lloyd, S., & Maccone, L.
Venue
Science
Published
2004-11-19
Volume
306
Issue
5700
Pages
1330-1336
ISSN
  • 0036-8075 (ISSN-L)
  • 1095-9203
OpenAlex
W1999664967
Cited by
3,038
References
10
FWCI
27.45
Type
journal article
Language
en
Open access
green

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CoChat. (2026). Citation check: Quantum-Enhanced Measurements: Beating the Standard Quantum Limit. https://app.cochat.ai/papers/10.1126/science.1104149
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Giovannetti, V., Lloyd, S., & Maccone, L. (2004). Quantum-Enhanced Measurements: Beating the Standard Quantum Limit. Science. https://doi.org/10.1126/science.1104149

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