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.

Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement


In continuously monitored systems the standard quantum limit is given by the trade-off between shot noise and back-action noise. In gravitational-wave detectors, such as Advanced LIGO, both contributions can be simultaneously squeezed in a broad frequency band by injecting a spectrum of squeezed vacuum states with a frequency-dependent squeeze angle. This approach requires setting up an additional long baseline, low-loss filter cavity in a vacuum system at the detector’s site. Here, we show that the need for such a filter cavity can be eliminated, by exploiting Einstein–Podolsky–Rosen (EPR)-entangled signals and idler beams. By harnessing their mutual quantum correlations and the difference in the way each beam propagates in the interferometer, we can engineer the input signal beam to have the appropriate frequency-dependent conditional squeezing once the out-going idler beam is detected. Our proposal is appropriate for all future gravitational-wave detectors for achieving sensitivities beyond the standard quantum limit.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Sensitivity of an Advanced LIGO-type gravitational-wave detector driven by squeezed vacuum (6 dB squeeze degree is chosen for comparing the 5% input/output loss case in Fig. 4) with a fixed squeezing angle.
Figure 2: Optical configuration for noise suppression via EPR entanglement.
Figure 3: The differential mode of the interferometer as seen by the signal (upper panel) and idler (lower panel) beams.
Figure 4: Sensitivity enhancement.
Figure 5: Spectral decomposition of EPR-entangled beams (upper panel) and the quantum statics of the signal and idler beams (lower panel).


  1. 1

    Abbott, B. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  2. 2

    Punturo, M. et al. The Einstein telescope: a third-generation gravitational wave observatory. Class. Quant. Gravity 27, 194002 (2010).

    ADS  Article  Google Scholar 

  3. 3

    Danilishin, S. & Khalili, F. Y. Quantum measurement theory in gravitational-wave detectors. Living Rev. Relativ. 15, 5 (2012).

    ADS  Article  MATH  Google Scholar 

  4. 4

    Miao, H., Yang, H., Adhikari, R. X. & Chen, Y. Quantum limits of interferometer topologies for gravitational radiation detection. Class. Quant. Gravity 31, 165010 (2014).

    ADS  Article  MATH  Google Scholar 

  5. 5

    Dwyer, S. et al. Gravitational wave detector with cosmological reach. Phys. Rev. D 91, 082001 (2015).

    ADS  Google Scholar 

  6. 6

    Abbott, B. et al. Exploring the sensitivity of next generation gravitational wave detectors. Class. Quant. Gravity 34, 044001 (2017).

    ADS  Article  Google Scholar 

  7. 7

    Sathyaprakash, B. et al. Scientific objectives of Einstein telescope. Class. Quant. Gravity 29, 124013 (2012).

    ADS  Article  Google Scholar 

  8. 8

    Tso, R., Isi, M., Chen, Y. & Stein, L. Modeling the dispersion and polarization content of gravitational waves for tests of general relativity. In Seventh Meeting on CPT and Lorentz Symmetry. Preprint at (2016).

  9. 9

    Kostelecky, A. & Mewes, M. Testing local Lorentz invariance with gravitational waves. Phys. Lett. B 757, 510–514 (2016).

    ADS  Article  MATH  Google Scholar 

  10. 10

    Lasky, P., Thrane, E., Levin, Y., Blackman, J. & Chen, Y. Detecting gravitational-wave memory with LIGO: implications of GW150914. Phys. Rev. Lett. 117, 061102 (2016).

    ADS  Article  Google Scholar 

  11. 11

    Berti, E. Astrophysical black holes as natural laboratories for fundamental physics and strong-field gravity. Braz. J. Phys. 43, 341 (2013).

    ADS  Article  Google Scholar 

  12. 12

    Chu, Q. et al. Capturing the electromagnetic counterparts of binary neutron star mergers through low-latency gravitational wave triggers. Mon. Not. R. Astron. Soc. 459, 121–139 (2016).

    ADS  Article  Google Scholar 

  13. 13

    Metzger, B. D. & Berger, E. What is the most promising electromagnetic counterpart of a neutron star binary merger? Astrophys. J. 746, 48 (2012).

    ADS  Article  Google Scholar 

  14. 14

    Aasi, J. et al. Constraints on cosmic strings from the LIGO-Virgo gravitational-wave detectors. Phys. Rev. Lett. 112, 131101 (2014).

    ADS  Article  Google Scholar 

  15. 15

    Drever, R. W. P., Hough, J., Edelstein, W. A., Pugh, J. R. & Martin, W. in Experimental Gravitation 365 (ed. Bertotii, B.) (Accademia Nazionale dei Lincei., 1976).

    Google Scholar 

  16. 16

    Braginsky, V. B. & Vorontsov, Y. I. Quantum-mechanical restrictions in macroscopic measurements and modern experimental devices. Sov. Phys. Usp. 17, 644–650 (1975).

    ADS  Article  Google Scholar 

  17. 17

    Weiss, R. Sources of Gravitational Radiation (Cambridge Univ. Press, 1979).

    Google Scholar 

  18. 18

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

    ADS  Article  Google Scholar 

  19. 19

    Kimble, H. J., Levin, Y., Matsko, A. B., Thorne, K. S. & Vyatchanin, S. P. Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics. Phys. Rev. D 65, 022002 (2001).

    ADS  Article  Google Scholar 

  20. 20

    Buonanno, A. & Chen, Y. Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors. Phys. Rev. D 64, 042006 (2001).

    ADS  Article  Google Scholar 

  21. 21

    Buonanno, A. & Chen, Y. Scaling law in signal recycled laser-interferometer gravitational-wave detectors. Phys. Rev. D 67, 062002 (2003).

    ADS  Article  Google Scholar 

  22. 22

    Unruh, W. G. Quantum Noise in the Interferometer Detector 647 (Plenum Press, 1983).

    Google Scholar 

  23. 23

    Schnabel, R., Mavalvala, N., McClelland, D. E. & Lam, P. K. Quantum metrology for gravitational wave astronomy. Nat. Commun. 1, 121 (2010).

    ADS  Article  Google Scholar 

  24. 24

    LIGO Instrument Science White Paper Technical report (2015).

  25. 25

    Vahlbruch, H. et al. Observation of squeezed light with 10-dB quantum-noise reduction. Phys. Rev. Lett. 100, 033602 (2009).

    ADS  Article  Google Scholar 

  26. 26

    Mehmet, M. et al. Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB. Opt. Express 19, 25763 (2011).

    ADS  Article  Google Scholar 

  27. 27

    Chua, S. S. Y. et al. Backscatter tolerant squeezed light source for advanced gravitational-wave detectors. Opt. Lett. 36, 4680–4682 (2011).

    ADS  Article  Google Scholar 

  28. 28

    Stefszky, M. S. et al. Balanced homodyne detection of optical quantum states at audio-band frequencies and below. Class. Quant. Gravity 29, 145015 (2012).

    ADS  Article  Google Scholar 

  29. 29

    McKenzie, K. et al. Squeezing in the audio gravitational-wave detection band. Phys. Rev. Lett. 93, 161105 (2004).

    ADS  Article  Google Scholar 

  30. 30

    Vahlbruch, H., Mehmet, M., Danzmann, K. & Schnabel, R. Detection of 15 dB squeezed states of light and their application for the absolute calibration of photo-electric quantum efficiency. Phys. Rev. Lett. 117, 110801 (2016).

    ADS  Article  Google Scholar 

  31. 31

    Abbott, B. et al. A gravitational wave observatory operating beyond the quantum shot-noise limit. Nat. Phys. 7, 962 (2011).

    Article  Google Scholar 

  32. 32

    Abbott, B. et al. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photon. 7, 613 (2013).

    ADS  MathSciNet  Article  Google Scholar 

  33. 33

    Jaekel, M. T. & Reynaud, S. Quantum limits in interferometer measurement. Europhys. Lett. 13, 301 (1990).

    ADS  Article  Google Scholar 

  34. 34

    Chelkowski, S. et al. Experimental characterization of frequency-dependent squeezed light. Phys. Rev. A 71, 013806 (2005).

    ADS  Article  Google Scholar 

  35. 35

    Evans, M., Barsotti, L., Kwee, P., Harms, J. & Miao, H. Realistic filter cavities for advanced gravitational wave detectors. Phys. Rev. D 88, 022002 (2013).

    ADS  Article  Google Scholar 

  36. 36

    Khalili, F. Y. Quantum variational measurement in the next generation gravitational-wave detectors. Phys. Rev. D 76, 102002 (2007).

    ADS  Article  Google Scholar 

  37. 37

    Khalili, F. Y. Optimal configurations of filter cavity in future gravitational-wave detectors. Phys. Rev. D 81, 122002 (2010).

    ADS  Article  Google Scholar 

  38. 38

    Isogai, T., Miller, J., Kwee, P., Barsotti, L. & Evans, M. Loss in long-storage-time optical cavities. Opt. Express 21, 30114–30125 (2013).

    ADS  Article  Google Scholar 

  39. 39

    Kwee, P., Miller, J., Isogai, T., Barsotti, L. & Evans, M. Decoherence and degradation of squeezed states in quantum filter cavities. Phys. Rev. D 90, 062006 (2014).

    ADS  Article  Google Scholar 

  40. 40

    Caposcasa, E. et al. Estimation of losses in a 300 m filter cavity and quantum noise reduction in the kagra gravitational-wave detector. Phys. Rev. D 93, 082004 (2016).

    ADS  Article  Google Scholar 

  41. 41

    ET Science Team. Einstein gravitative wave telescope conceptual design study. ET-0106C-10 (2011).

  42. 42

    Mikhailov, E. E., Goda, K., Corbitt, T. & Mavalvala, N. Frequency-dependent squeeze-amplitude attenuation and squeeze-angle rotation by electromagnetically induced transparency for gravitational-wave interferometers. Phys. Rev. A 73, 053810 (2006).

    ADS  Article  Google Scholar 

  43. 43

    Ma, Y. et al. Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction. Phys. Rev. Lett. 113, 151102 (2014).

    ADS  Article  Google Scholar 

  44. 44

    Qin, J. et al. Classical demonstration of frequency-dependent noise ellipse rotation using optomechanically induced transparency. Phys. Rev. A 89, 041802(R) (2014).

    ADS  Article  Google Scholar 

  45. 45

    Zhang, J. Einstein–Podolsky–Rosen sideband entanglement in broadband squeezed light. Phys. Rev. A 67, 054302 (2003).

    ADS  Article  Google Scholar 

  46. 46

    Marino, A. M., Stroud, C. R., Wong, V., Bennink, R. S. & Boyd, R. W. Bichromatic local oscillator for detection of two-mode squeezed states of light. J. Opt. Soc. Am. B 24, 335–339 (2007).

    ADS  Article  Google Scholar 

  47. 47

    Hage, B., Samblowski, A. & Schnabel, R. Towards Einstein–Podolsky–Rosen quantum channel multiplexing. Phys. Rev. A 81, 062301 (2010).

    ADS  MathSciNet  Article  Google Scholar 

  48. 48

    Barsotti, L. LIGO: The A+ Upgrade LIGO Doc. G1601199-v2 (2016).

  49. 49

    Barsotti, L. Squeezing for Advanced LIGO LIGO Doc. G1401092-v1 (2014).

Download references


Research of Y.M., B.H.P. and Y.C. is supported by NSF grant PHY-1404569 and PHY-1506453, as well as the Institute for Quantum Information and Matter, a Physics Frontier Center. H.M. is supported by the Marie-Curie Fellowship and UK STFC Ernest Rutherford Fellowship. C.Z. would like to thank the support of Australian Research Council Discovery Project DP120104676 and DP120100898. R.S. is supported by DFG grant SCHN757/6 and by ERC grant 339897 (‘Mass Q’).

Author information




Y.M., H.M. and Y.C. formulated the idea; Y.M. performed the analysis of the idea and wrote the initial draft, which was later revised by Y.C.; B.H.P. checked Y.M.’s calculation; M.E., J.H., R.S. and C.Z. provided important experimental parameters for doing theoretical analysis and gave valuable comments on Y.M.’s calculations and initial/revised draft.

Corresponding author

Correspondence to Yiqiu Ma.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 626 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ma, Y., Miao, H., Pang, B. et al. Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement. Nature Phys 13, 776–780 (2017).

Download citation

Further reading


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