Skip to main content

Thank you for visiting 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.

  • Letter
  • Published:

Unconditional violation of the shot-noise limit in photonic quantum metrology


Interferometric phase measurement is widely used to precisely determine quantities such as length, speed and material properties1,2,3. Without quantum correlations, the best phase sensitivity \({\boldsymbol{\Delta }}{\boldsymbol{\phi }}\) achievable using n photons is the shot-noise limit, \({\boldsymbol{\Delta }}{\boldsymbol{\phi }}=1\,/\sqrt{{n}}\). Quantum-enhanced metrology promises better sensitivity, but, despite theoretical proposals stretching back decades3,4, no measurement using photonic (that is, definite photon number) quantum states has truly surpassed the shot-noise limit. Instead, all such demonstrations, by discounting photon loss, detector inefficiency or other imperfections, have considered only a subset of the photons used. Here, we use an ultrahigh-efficiency photon source and detectors to perform unconditional entanglement-enhanced photonic interferometry. Sampling a birefringent phase shift, we demonstrate precision beyond the shot-noise limit without artificially correcting our results for loss and imperfections. Our results enable quantum-enhanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances.

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

Fig. 1: Experimental set-up for the N = 2 NOON state optical interferometer.
Fig. 2: Experimentally measured output detection probability and the corresponding Fisher information.
Fig. 3: Experimentally measured phase estimate and phase uncertainty.

Similar content being viewed by others


  1. Caves, C. M. Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693–1708 (1981).

    Article  ADS  Google Scholar 

  2. Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control (Cambridge Univ. Press, 2009).

  3. Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011).

    Article  ADS  Google Scholar 

  4. Demkowicz-Dobrzański, R., Jarzyna, M. & Kołdyński, J. Chapter four-quantum limits in optical interferometry. Prog. Opt. 60, 345–435 (2015).

    Article  Google Scholar 

  5. Dowling, J. P. Quantum optical metrology—the lowdown on high-NOON states. Contemp. Phys. 49, 125–143 (2008).

    Article  ADS  Google Scholar 

  6. Wolfgramm, F., Vitelli, C., Beduini, F. A., Godbout, N. & Mitchell, M. W. Entanglement-enhanced probing of a delicate material system. Nat. Photon. 7, 28–32 (2013).

    Article  ADS  Google Scholar 

  7. Yonezawa, H. et al. Quantum-enhanced optical-phase tracking. Science 337, 1514–1517 (2012).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Aasi, J. et al. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photon. 7, 613–619 (2013).

    Article  ADS  Google Scholar 

  9. Xiang, G., Hofmann, H. & Pryde, G. J. Optimal multi-photon phase sensing with a single interference fringe. Sci. Rep. 3, 2684 (2013).

    Article  ADS  Google Scholar 

  10. Resch, K. J. et al. Time-reversal and super-resolving phase measurements. Phys. Rev. Lett. 98, 223601 (2007).

    Article  ADS  Google Scholar 

  11. Ou, Z. Y., Zou, X. Y., Wang, L. J. & Mandel, L. Experiment on nonclassical fourth-order interference. Phys. Rev. A 42, 2957–2965 (1990).

    Article  ADS  Google Scholar 

  12. Rarity, J. G. et al. Two-photon interference in a Mach–Zehnder interferometer. Phys. Rev. Lett. 65, 1348–1351 (1990).

    Article  ADS  Google Scholar 

  13. Fonseca, E. J. S., Monken, C. H. & Pádua, S. Measurement of the de Broglie wavelength of a multiphoton wave packet. Phys. Rev. Lett. 82, 2868–2871 (1999).

    Article  ADS  Google Scholar 

  14. Eisenberg, H. S., Hodelin, J. F., Khoury, G. & Bouwmeester, D. Multiphoton path entanglement by nonlocal bunching. Phys. Rev. Lett. 94, 090502 (2005).

    Article  ADS  Google Scholar 

  15. Mitchell, M. W., Lundeen, J. S. & Steinberg, A. M. Super-resolving phase measurements with a multiphoton entangled state. Nature 429, 161–164 (2004).

    Article  ADS  Google Scholar 

  16. Walther, P. et al. De Broglie wavelength of a non-local four-photon state. Nature 429, 158–161 (2004).

    Article  ADS  Google Scholar 

  17. Nagata, T., Okamoto, R., O’Brien, J. L., Sasaki, K. & Takeuchi, S. Beating the standard quantum limit with four-entangled photons. Science 316, 726–729 (2007).

    Article  ADS  Google Scholar 

  18. Gao, W.-B. et al. Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state. Nat. Phys. 6, 331–335 (2010).

    Article  Google Scholar 

  19. Wang, X.-L. et al. Experimental ten-photon entanglement. Phys. Rev. Lett. 117, 210502 (2016).

    Article  ADS  Google Scholar 

  20. Okamoto, R. et al. Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers. New J. Phys. 10, 073033 (2008).

    Article  ADS  Google Scholar 

  21. Datta, A. et al. Quantum metrology with imperfect states and detectors. Phys. Rev. A 83, 063836 (2011).

    Article  ADS  Google Scholar 

  22. Weston, M. M. et al. Efficient and pure femtosecond-pulse-length source of polarization-entangled photons. Opt. Express 24, 10869–10879 (2016).

    Article  ADS  Google Scholar 

  23. Marsili, F. et al. Detecting single infrared photons with 93% system efficiency. Nat. Photon. 7, 210–214 (2013).

    Article  ADS  Google Scholar 

  24. Klyshko, D. N. Use of two-photon light for absolute calibration of photoelectric detectors. Sov. J. Quantum Electron. 10, 1112–1116 (1980).

    Article  ADS  Google Scholar 

  25. Lita, A. E., Miller, A. J. & Nam, S. W. Counting near-infrared single-photons with 95% efficiency. Opt. Express 16, 3032–3040 (2008).

    Article  ADS  Google Scholar 

  26. Matthews, J. C. F. et al. Towards practical quantum metrology with photon counting. NPJ Quantum Inf. 2, 16023 (2016).

    Article  ADS  Google Scholar 

  27. Harder, G. et al. Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics. Phys. Rev. Lett. 116, 143601 (2016).

    Article  ADS  Google Scholar 

  28. Higgins, B. L., Berry, D. W., Bartlett, S. D., Wiseman, H. M. & Pryde, G. J. Entanglement-free Heisenberg-limited phase estimation. Nature 450, 393–396 (2007).

    Article  ADS  Google Scholar 

  29. Davison, A. C. & Hinkley, D. V. Bootstrap Methods and Their Application, Vol. 1 (Cambridge Univ. Press, 1997).

Download references


This work was supported by the Australian Research Council (grant DP140100648). The authors thank J. Ho for help with SNSPDs.

Author information

Authors and Affiliations



G.J.P. conceived the idea and supervised the project. S.S. and M.M.W. constructed and carried out the experiment with help from H.M.C. L.K.S., V.B.V. and S.W.N. developed the high-efficiency SNSPDs. All authors discussed the results and contributed to writing the manuscript.

Corresponding author

Correspondence to Geoff J. Pryde.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Slussarenko, S., Weston, M.M., Chrzanowski, H.M. et al. Unconditional violation of the shot-noise limit in photonic quantum metrology. Nature Photon 11, 700–703 (2017).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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