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.

Imaging with quantum states of light

Nature Reviews Physics volume 1, pages 367–380 (2019)Cite this article

Subjects

Abstract

The production of pairs of entangled photons simply by focusing a laser beam onto a crystal with a nonlinear optical response was used to test quantum mechanics and to open new approaches in imaging. The development of the latter was enabled by the emergence of single-photon-sensitive cameras that are able to characterize spatial correlations and high-dimensional entanglement. Thereby, new techniques emerged, such as ghost imaging of objects — in which the quantum correlations between photons reveal the image from photons that have never interacted with the object — or imaging with undetected photons by using nonlinear interferometers. In addition, quantum approaches in imaging can also lead to an improvement in the performance of conventional imaging systems. These improvements can be obtained by means of image contrast, resolution enhancement that exceeds the classical limit and acquisition of sub-shot-noise phase or amplitude images. In this Review, we discuss the application of quantum states of light for advanced imaging techniques.

Key points

  • Improvements in available camera technologies have enabled the efficient detection and characterization of quantum behaviours in continuous spatial variables.

  • The use of cameras in the context of quantum optics allows the detection and use of high-dimensional quantum states.

  • Quantum states of light can be harnessed to implement quantum imaging protocols that allow improved imaging over classical techniques; such protocols can lead to improved estimation of the transmission, reflectance and phase of an imaged object, in addition to offering improved resolution images of the object.

  • Quantum imaging techniques allow new types of imaging, such as ghost imaging, quantum imaging with undetected photons or the implementation of interaction-free measurements in the context of imaging.

  • Sources of pairs of photons with different wavelengths allow the lack of high-fidelity detectors at exotic wavelengths to be overcome through ghost imaging techniques and quantum nonlinear interferometric imaging techniques.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

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

Fig. 1: Generation and detection of quantum correlations in spontaneous parametric down-conversion.
Fig. 2: Experimental test of Einstein–Podolsky–Rosen paradox in images.
Fig. 3: Sub-shot-noise quantum imaging.
Fig. 4: Principle of quantum lithography.
Fig. 5: Non-degenerate quantum ghost imaging.
Fig. 6: Quantum imaging with undetected photons.

Similar content being viewed by others

References

  1. Franken, P. A., Hill, A. E., Peters, C. W. & Weinreich, G. Generation of optical harmonics. Phys. Rev. Lett. 7, 118–119 (1961).

    ADS  Google Scholar 

  2. Wang, C. C. & Racette, G. W. Measurement of parametric gain accompanying optical difference frequency generation. Appl. Phys. Lett. 6, 169–171 (1965).

    ADS  Google Scholar 

  3. Giordmaine, J. & Miller, R. C. Tunable coherent parametric oscillation in LiNbO3 at optical frequencies. Phys. Rev. Lett. 14, 973–976 (1965).

    ADS  Google Scholar 

  4. Kocher, C. A. & Commins, E. D. Polarization correlation of photons emitted in an atomic cascade. Phys. Rev. Lett. 18, 575–577 (1967).

    ADS  Google Scholar 

  5. Freedman, S. J. & Clauser, J. F. Experimental test of local hidden-variable theories. Phys. Rev. Lett. 28, 938–941 (1972).

    ADS  Google Scholar 

  6. Aspect, A., Dalibard, J. & Roger, G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982).

    ADS  MathSciNet  Google Scholar 

  7. Louisell, W., Yariv, A. & Siegman, A. Quantum fluctuations and noise in parametric processes. I. Phys. Rev. 124, 1646–1654 (1961).

    ADS  MATH  Google Scholar 

  8. Haus, H. A. & Mullen, J. Quantum noise in linear amplifiers. Phys. Rev. 128, 2407–2413 (1962).

    ADS  Google Scholar 

  9. Klyshko, D. Scattering of light in a medium with nonlinear polarizability. Sov. Phys. JETP 28, 522–526 (1969).

    ADS  Google Scholar 

  10. Harris, S., Oshman, M. & Byer, R. Observation of tunable optical parametric fluorescence. Phys. Rev. Lett. 18, 732–734 (1967).

    ADS  Google Scholar 

  11. Akhmanov, S., Fadeev, V., Khokhlov, R. & Chunaev, O. Quantum noise in parametric light amplifiers. ZhETF Pisma Redaktsiiu 6, 575–578 (1967).

    ADS  Google Scholar 

  12. Burnham, D. C. & Weinberg, D. L. Observation of simultaneity in parametric production of optical photon pairs. Phys. Rev. Lett. 25, 84–87 (1970).

    ADS  Google Scholar 

  13. Ghosh, R. & Mandel, L. Observation of nonclassical effects in the interference of two photons. Phys. Rev. Lett. 59, 1903–1905 (1987).

    ADS  Google Scholar 

  14. Ou, Z. & Mandel, L. Violation of Bell’s inequality and classical probability in a two-photon correlation experiment. Phys. Rev. Lett. 61, 50–53 (1988).

    ADS  MathSciNet  Google Scholar 

  15. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

    ADS  Google Scholar 

  16. Shih, Y. Entangled biphoton source-property and preparation. Rep. Prog. Phys. 66, 1009–1044 (2003).

    ADS  MathSciNet  Google Scholar 

  17. Genovese, M. Research on hidden variable theories: a review of recent progresses. Phys. Rep. 413, 319–396 (2005).

    ADS  MathSciNet  Google Scholar 

  18. Hong, C.-K., Ou, Z.-Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987).

    ADS  Google Scholar 

  19. Kim, Y.-H., Yu, R., Kulik, S. P., Shih, Y. & Scully, M. O. Delayed “choice” quantum eraser. Phys. Rev. Lett. 84, 1–5 (2000).

    ADS  Google Scholar 

  20. Ma, X.-S., Kofler, J. & Zeilinger, A. Delayed-choice gedanken experiments and their realizations. Rev. Mod. Phys. 88, 015005 (2016).

    ADS  Google Scholar 

  21. Ren, J.-G. et al. Ground-to-satellite quantum teleportation. Nature 549, 70–73 (2017).

    ADS  Google Scholar 

  22. O’Brien, J. L., Pryde, G. J., White, A. G., Ralph, T. C. & Branning, D. Demonstration of an all-optical quantum controlled-not gate. Nature 426, 264–267 (2003).

    ADS  Google Scholar 

  23. Qiang, X. et al. Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nat. Photon. 12, 534–539 (2018).

    ADS  Google Scholar 

  24. Lo, H.-K., Curty, M. & Tamaki, K. Secure quantum key distribution. Nat. Photon. 8, 595–604 (2014).

    ADS  Google Scholar 

  25. Shalm, L. K. et al. Strong loophole-free test of local realism. Phys. Rev. Lett. 115, 250402 (2015).

    ADS  Google Scholar 

  26. Giustina, M. et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Phys. Rev. Lett. 115, 250401 (2015).

    ADS  Google Scholar 

  27. Howell, J. C., Bennink, R. S., Bentley, S. J. & Boyd, R. Realization of the Einstein–Podolsky–Rosen paradox using momentum-and position-entangled photons from spontaneous parametric down conversion. Phys. Rev. Lett. 92, 210403 (2004).

    ADS  Google Scholar 

  28. Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935).

    ADS  MATH  Google Scholar 

  29. Klyshko, D. Photons and Nonlinear Optics (CRC Press, 1988).

  30. Jost, B. M., Sergienko, A. V., Abouraddy, A. F., Saleh, B. E. & Teich, M. C. Spatial correlations of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera. Opt. Express 3, 81–88 (1998).

    ADS  Google Scholar 

  31. Basden, A. G., Haniff, C. & Mackay, C. Photon counting strategies with low-light-level CCDs. Mon. Not. R. Astron. Soc. 345, 985–991 (2003).

    ADS  Google Scholar 

  32. Rarity, J. & Tapster, P. Experimental violation of Bell’s inequality based on phase and momentum. Phys. Rev. Lett. 64, 2495–2498 (1990).

    ADS  Google Scholar 

  33. Pittman, T., Shih, Y., Strekalov, D. & Sergienko, A. Optical imaging by means of two-photon quantum entanglement. Phys. Rev. A 52, R3429–R3432 (1995).

    ADS  Google Scholar 

  34. Strekalov, D. V., Sergienko, A. V., Klyshko, D. N. & Shih, Y. H. Observation of two-photon ghost interference and diffraction. Phys. Rev. Lett. 74, 3600–3603 (1995).

    ADS  Google Scholar 

  35. Devaux, F. & Lantz, E. Spatial and temporal properties of parametric fluorescence around degeneracy in a type I LBO crystal. Eur. Phys. J. D 8, 117–124 (2000).

    ADS  Google Scholar 

  36. Couteau, C. Spontaneous parametric down-conversion. Contemp. Phys. 59, 291–304 (2018).

    ADS  Google Scholar 

  37. Boyd, R. W. Nonlinear Optics (Elsevier, 2003).

  38. Jakeman, E. & Walker, J. Analysis of a method for the generation of light with sub-poissonian photon statistics. Opt. Commun. 55, 219–222 (1985).

    ADS  Google Scholar 

  39. Jakeman, E. & Rarity, J. The use of pair production processes to reduce quantum noise in transmission measurements. Opt. Commun. 59, 219–223 (1986).

    ADS  Google Scholar 

  40. Rarity, J., Tapster, P. & Jakeman, E. Observation of sub-Poissonian light in parametric downconversion. Opt. Commun. 62, 201–206 (1987).

    ADS  Google Scholar 

  41. Heidmann, A. et al. Observation of quantum noise reduction on twin laser beams. Phys. Rev. Lett. 59, 2555–2557 (1987).

    ADS  Google Scholar 

  42. Nabors, C. & Shelby, R. Two-color squeezing and sub-shot-noise signal recovery in doubly resonant optical parametric oscillators. Phys. Rev. A 42, 556–559 (1990).

    ADS  Google Scholar 

  43. Tapster, P., Seward, S. & Rarity, J. Sub-shot-noise measurement of modulated absorption using parametric down-conversion. Phys. Rev. A 44, 3266–3269 (1991).

    ADS  Google Scholar 

  44. Ribeiro, P. S. & C. Schwob, A. Sub-shot-noise high-sensitivity spectroscopy with optical parametric oscillator twin beams. Opt. Lett. 22, 1893–1895 (1997).

    ADS  Google Scholar 

  45. Bondani, M., Allevi, A., Zambra, G., Paris, M. G. & Andreoni, A. Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light. Phys. Rev. A 76, 013833 (2007).

    ADS  Google Scholar 

  46. Iskhakov, T., Chekhova, M. V. & Leuchs, G. Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum. Phys. Rev. Lett. 102, 183602 (2009).

    ADS  Google Scholar 

  47. Jedrkiewicz, O. et al. Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion. Phys. Rev. Lett. 93, 243601 (2004).

    ADS  Google Scholar 

  48. Jedrkiewicz, O. et al. Quantum spatial correlations in high-gain parametric down-conversion measured by means of a CCD camera. J. Mod. Opt. 53, 575–595 (2006).

    ADS  Google Scholar 

  49. Blanchet, J.-L., Devaux, F., Furfaro, L. & Lantz, E. Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime. Phys. Rev. Lett. 101, 233604 (2008).

    ADS  Google Scholar 

  50. Brambilla, E., Caspani, L., Jedrkiewicz, O., Lugiato, L. & Gatti, A. High-sensitivity imaging with multi-mode twin beams. Phys. Rev. A 77, 053807 (2008).

    ADS  Google Scholar 

  51. Brida, G. et al. Measurement of sub-shot-noise spatial correlations without background subtraction. Phys. Rev. Lett. 102, 213602 (2009).

    ADS  Google Scholar 

  52. Brida, G., Genovese, M. & Berchera, I. R. Experimental realization of sub-shot-noise quantum imaging. Nat. Photon. 4, 227–230 (2010).

    ADS  Google Scholar 

  53. Jerram, P. et al. in Proceedings of SPIE Vol. 4306 (eds Sampat, N. et al.) 178–187 (International Society for Optics and Photonics, 2001).

  54. Lantz, E., Blanchet, J.-L., Furfaro, L. & Devaux, F. Multi-imaging and Bayesian estimation for photon counting with EMCCDs. Mon. Not. R. Astron. Soc. 386, 2262–2270 (2008).

    ADS  Google Scholar 

  55. Zhang, L., Neves, L., Lundeen, J. S. & Walmsley, I. A. A characterization of the single-photon sensitivity of an electron multiplying charge-coupled device. J. Phys. B 42, 114011 (2009).

    ADS  Google Scholar 

  56. Blanchet, J.-L., Devaux, F., Furfaro, L. & Lantz, E. Purely spatial coincidences of twin photons in parametric spontaneous down-conversion. Phys. Rev. A 81, 043825 (2010).

    ADS  Google Scholar 

  57. Toninelli, E. et al. Sub-shot-noise shadow sensing with quantum correlations. Opt. Express 25, 21826–21840 (2017).

    ADS  Google Scholar 

  58. Reichert, M., Defienne, H., Sun, X. & Fleischer, J. W. Biphoton transmission through non-unitary objects. J. Opt. 19, 044004 (2017).

    ADS  Google Scholar 

  59. Reichert, M., Defienne, H. & Fleischer, J. W. Massively parallel coincidence counting of high-dimensional entangled states. Sci. Rep. 8, 7925 (2018).

    ADS  Google Scholar 

  60. Devaux, F., Mougin-Sisini, J., Moreau, P.-A. & Lantz, E. Towards the evidence of a purely spatial Einstein–Podolsky–Rosen paradox in images: measurement scheme and first experimental results. Eur. Phys. J. D 66, 192 (2012).

    ADS  Google Scholar 

  61. Moreau, P.-A., Mougin-Sisini, J., Devaux, F. & Lantz, E. Realization of the purely spatial Einstein–Podolsky–Rosen paradox in full-field images of spontaneous parametric down-conversion. Phys. Rev. A 86, 010101 (2012).

    ADS  Google Scholar 

  62. Edgar, M. P. et al. Imaging high-dimensional spatial entanglement with a camera. Nat. Commun. 3, 984 (2012).

    Google Scholar 

  63. Moreau, P.-A., Devaux, F. & Lantz, E. Einstein–Podolsky–Rosen paradox in twin images. Phys. Rev. Lett. 113, 160401 (2014).

  64. Lantz, E., Denis, S., Moreau, P.-A. & Devaux, F. Einstein–Podolsky–Rosen paradox in single pairs of images. Opt. Express 23, 26472–26478 (2015).

    ADS  Google Scholar 

  65. Takhar, D. et al. in Proceedings of SPIE Vol. 6065 (eds Bouman, C. A., Miller, E. L. & Pollak, I.) 606509 (International Society for Optics and Photonics, 2006).

  66. Duarte, M. F. et al. Single-pixel imaging via compressive sampling. IEEE Signal Process. Mag. 25, 83–91 (2008).

    ADS  Google Scholar 

  67. Howland, G. A. & Howell, J. C. Efficient high-dimensional entanglement imaging with a compressive-sensing double-pixel camera. Phys. Rev. X 3, 011013 (2013).

    Google Scholar 

  68. Schneeloch, J., Dixon, P. B., Howland, G. A., Broadbent, C. J. & Howell, J. C. Violation of continuous-variable Einstein–Podolsky–Rosen steering with discrete measurements. Phys. Rev. Lett. 110, 130407 (2013).

    ADS  Google Scholar 

  69. Lampton, M. The microchannel image intensifier. Sci. Am. 245, 62–71 (1981).

    ADS  Google Scholar 

  70. Abouraddy, A. F., Nasr, M., Saleh, B. E., Sergienko, A. V. & Teich, M. C. Demonstration of the complementarity of one-and two-photon interference. Phys. Rev. A 63, 063803 (2001).

    ADS  Google Scholar 

  71. Pires, H. D. L., Monken, C. H. & van Exter, M. P. Direct measurement of transverse-mode entanglement in two-photon states. Phys. Rev. A 80, 022307 (2009).

    ADS  Google Scholar 

  72. Aspden, R. S., Tasca, D. S., Boyd, R. W. & Padgett, M. J. EPR-based ghost imaging using a single-photon-sensitive camera. New J. Phys. 15, 073032 (2013).

    ADS  Google Scholar 

  73. Fickler, R., Krenn, M., Lapkiewicz, R., Ramelow, S. & Zeilinger, A. Real-time imaging of quantum entanglement. Sci. Rep. 3, 1914 (2013).

    ADS  Google Scholar 

  74. Jachura, M. & Chrapkiewicz, R. Shot-by-shot imaging of Hong–Ou–Mandel interference with an intensified sCMOS camera. Opt. Lett. 40, 1540–1543 (2015).

    ADS  Google Scholar 

  75. Chrapkiewicz, R., Wasilewski, W. & Banaszek, K. High-fidelity spatially resolved multiphoton counting for quantum imaging applications. Opt. Lett. 39, 5090–5093 (2014).

    ADS  Google Scholar 

  76. Chrapkiewicz, R., Jachura, M., Banaszek, K. & Wasilewski, W. Hologram of a single photon. Nat. Photon. 10, 576–579 (2016).

    ADS  Google Scholar 

  77. Jachura, M., Chrapkiewicz, R., Demkowicz-Dobrzański, R., Wasilewski, W. & Banaszek, K. Mode engineering for realistic quantum-enhanced interferometry. Nat. Commun. 7, 11411 (2016).

    ADS  Google Scholar 

  78. Parniak, M. et al. Wavevector multiplexed atomic quantum memory via spatially-resolved single-photon detection. Nat. Commun. 8, 2140 (2017).

    ADS  Google Scholar 

  79. Guerrieri, F., Tisa, S., Tosi, A. & Zappa, F. Two-dimensional spad imaging camera for photon counting. IEEE Photon. J. 2, 759–774 (2010).

    ADS  Google Scholar 

  80. Guerrieri, F. et al. Sub-Rayleigh imaging via N-photon detection. Phys. Rev. Lett. 105, 163602 (2010).

    ADS  Google Scholar 

  81. Veerappan, C. et al. A 160×128 single-photon image sensor with on-pixel 55ps 10b time-to-digital converter. In Solid-State Circuits Conference Digest of Technical Papers (ISSCC), 2011 IEEE International 312–314 (IEEE, 2011).

  82. Gariepy, G. et al. Single-photon sensitive light-in-fight imaging. Nat. Commun. 6, 6021 (2015).

    Google Scholar 

  83. Miki, S., Yamashita, T., Wang, Z. & Terai, H. A 64-pixel nbtin superconducting nanowire single-photon detector array for spatially resolved photon detection. Opt. Express 22, 7811–7820 (2014).

    ADS  Google Scholar 

  84. Allman, M. S. et al. A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout. Appl. Phys. Lett. 106, 192601 (2015).

    ADS  Google Scholar 

  85. Ma, J., Masoodian, S., Starkey, D. A. & Fossum, E. R. Photon-number-resolving megapixel image sensor at room temperature without avalanche gain. Optica 4, 1474–1481 (2017).

    Google Scholar 

  86. Andersen, U. L., Gehring, T., Marquardt, C. & Leuchs, G. 30 years of squeezed light generation. Phys. Scr. 91, 053001 (2016).

    ADS  Google Scholar 

  87. Schnabel, R. Squeezed states of light and their applications in laser interferometers. Phys. Rep. 684, 1–51 (2017).

    ADS  MathSciNet  MATH  Google Scholar 

  88. Mandel, L. Physical significance of operators in quantum optics. Phys. Rev. 136, B1221 (1964).

    ADS  MathSciNet  Google Scholar 

  89. Stoler, D. Photon antibunching and possible ways to observe it. Phys. Rev. Lett. 33, 1397–1400 (1974).

    ADS  Google Scholar 

  90. Hollenhorst, J. N. Quantum limits on resonant-mass gravitational-radiation detectors. Phys. Rev. D 19, 1669–1679 (1979).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  92. Snyder, J. J., Giacobino, E., Fabre, C., Heidmann, A. & Ducloy, M. Sub-shot-noise measurements using the beat note between quantum-correlated photon beams. J. Opt. Soc. Am. B 7, 2132–2136 (1990).

    ADS  Google Scholar 

  93. Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330–1336 (2004).

    ADS  Google Scholar 

  94. Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).

    ADS  MathSciNet  Google Scholar 

  95. Caves, C. M., Thorne, K. S., Drever, R. W., Sandberg, V. D. & Zimmermann, M. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys. 52, 341–392 (1980).

    ADS  Google Scholar 

  96. Abadie, J. et al. A gravitational wave observatory operating beyond the quantum shot-noise limit. Nat. Phys. 7, 962–965 (2011).

    Google Scholar 

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

    ADS  Google Scholar 

  98. Taylor, M. A. & Bowen, W. P. Quantum metrology and its application in biology. Phys. Rep. 615, 1–59 (2016).

    ADS  MathSciNet  Google Scholar 

  99. 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).

    ADS  Google Scholar 

  100. Davidovich, L. Sub-poissonian processes in quantum optics. Rev. Mod. Phys. 68, 127–173 (1996).

    ADS  MathSciNet  Google Scholar 

  101. Xiao, M., Wu, L.-A. & Kimble, H. Detection of amplitude modulation with squeezed light for sensitivity beyond the shot-noise limit. Opt. Lett. 13, 476–478 (1988).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  103. Kolobov, M. I. & Fabre, C. Quantum limits on optical resolution. Phys. Rev. Lett. 85, 3789 (2000).

    ADS  Google Scholar 

  104. Treps, N. et al. Surpassing the standard quantum limit for optical imaging using nonclassical multimode light. Phys. Rev. Lett. 88, 203601 (2002).

    ADS  Google Scholar 

  105. Treps, N. et al. A quantum laser pointer. Science 301, 940–943 (2003).

    ADS  Google Scholar 

  106. Boyer, V., Marino, A. M., Pooser, R. C. & Lett, P. D. Entangled images from four-wave mixing. Science 321, 544–547 (2008).

    ADS  Google Scholar 

  107. Lassen, M., Leuchs, G. & Andersen, U. L. Continuous variable entanglement and squeezing of orbital angular momentum states. Phys. Rev. Lett. 102, 163602 (2009).

    ADS  Google Scholar 

  108. Wagner, K. et al. Entangling the spatial properties of laser beams. Science 321, 541–543 (2008).

    ADS  Google Scholar 

  109. Sabines-Chesterking, J. et al. Sub-shot-noise transmission measurement enabled by active feed-forward of heralded single photons. Phys. Rev. Appl. 8, 014016 (2017).

    ADS  Google Scholar 

  110. Samantaray, N., Ruo-Berchera, I., Meda, A. & Genovese, M. Realization of the first sub-shot-noise wide field microscope. Light Sci. Appl. 6, e17005 (2017).

    ADS  Google Scholar 

  111. Moreau, P.-A. et al. Demonstrating an absolute quantum advantage in direct absorption measurement. Sci. Rep. 7, 6256 (2017).

    ADS  Google Scholar 

  112. Losero, E., Ruo-Berchera, I., Meda, A., Avella, A. & Genovese, M. Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams. Sci. Rep. 8, 7431 (2018).

    ADS  Google Scholar 

  113. Iskhakov, T. S. et al. Heralded source of bright multi-mode mesoscopic sub-Poissonian light. Opt. Lett. 41, 2149–2152 (2016).

    ADS  Google Scholar 

  114. Nagata, T. et al. Beating the standard quantum limit with four-entangled photons. Science 316, 726–729 (2007).

    ADS  Google Scholar 

  115. Jacobson, J., Björk, G., Chuang, I. & Yamamoto, Y. Photonic de Broglie waves. Phys. Rev. Lett. 74, 4835–4838 (1995).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  117. Ono, T., Okamoto, R. & Takeuchi, S. An entanglement-enhanced microscope. Nat. Commun. 4, 3426 (2013).

    Google Scholar 

  118. Yurke, B., McCall, S. L. & Klauder, J. R. SU(2) and SU(1,1) interferometers. Phys. Rev. A 33, 4033–4054 (1986).

    ADS  Google Scholar 

  119. Leonhardt, U. Quantum statistics of a two-mode SU(1,1) interferometer. Phys. Rev. A 49, 1231–1242 (1994).

    ADS  Google Scholar 

  120. Plick, W. N., Dowling, J. P. & Agarwal, G. S. Coherent-light-boosted, sub-shot noise, quantum interferometry. New J. Phys. 12, 083014 (2010).

    ADS  Google Scholar 

  121. Marino, A. M., Trejo, N. C. & Lett, P. D. Effect of losses on the performance of an SU(1,1) interferometer. Phys. Rev. A 86, 023844 (2012).

    ADS  Google Scholar 

  122. Ou, Z. Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer. Phys. Rev. A 85, 023815 (2012).

    ADS  Google Scholar 

  123. Jing, J., Liu, C., Zhou, Z., Ou, Z. & Zhang, W. Realization of a nonlinear interferometer with parametric amplifiers. Appl. Phys. Lett. 99, 011110 (2011).

    ADS  Google Scholar 

  124. Hudelist, F. et al. Quantum metrology with parametric amplifier-based photon correlation interferometers. Nat. Commun. 5, 3049 (2014).

    Google Scholar 

  125. Manceau, M., Leuchs, G., Khalili, F. & Chekhova, M. Detection loss tolerant supersensitive phase measurement with an SU(1,1) interferometer. Phys. Rev. Lett. 119, 223604 (2017).

    ADS  Google Scholar 

  126. Morris, P. A., Aspden, R. S., Bell, J. E., Boyd, R. W. & Padgett, M. J. Imaging with a small number of photons. Nat. Commun. 6, 5913 (2015).

    ADS  Google Scholar 

  127. Lanzagorta, M. Quantum radar. Synth. Lect. Quantum Comput. 3, 1–139 (2011).

    Google Scholar 

  128. Lloyd, S. Enhanced sensitivity of photodetection via quantum illumination. Science 321, 1463–1465 (2008).

    ADS  Google Scholar 

  129. Giovannetti, V., Lloyd, S., Maccone, L. & Shapiro, J. H. Sub-Rayleigh-diffraction-bound quantum imaging. Phys. Rev. A 79, 013827 (2009).

    ADS  Google Scholar 

  130. Mouradian, S., Wong, F. N. & Shapiro, J. H. Achieving sub-Rayleigh resolution via thresholding. Opt. Express 19, 5480–5488 (2011).

    ADS  Google Scholar 

  131. Schwartz, O. & Oron, D. Improved resolution in fluorescence microscopy using quantum correlations. Phys. Rev. A 85, 033812 (2012).

    ADS  Google Scholar 

  132. Schwartz, O. et al. Superresolution microscopy with quantum emitters. Nano Lett. 13, 5832–5836 (2013).

    ADS  Google Scholar 

  133. Israel, Y., Tenne, R., Oron, D. & Silberberg, Y. Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera. Nat. Commun. 8, 14786 (2017).

    ADS  Google Scholar 

  134. Monticone, D. G. et al. Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics. Phys. Rev. Lett. 113, 143602 (2014).

    ADS  Google Scholar 

  135. Classen, A., von Zanthier, J., Scully, M. O. & Agarwal, G. S. Superresolution via structured illumination quantum correlation microscopy. Optica 4, 580–587 (2017).

    Google Scholar 

  136. Tenne, R. et al. Super-resolution enhancement by quantum image scanning microscopy. Nat. Photon. 13, 116–122 (2019).

    ADS  Google Scholar 

  137. Tsang, M., Nair, R. & Lu, X.-M. Quantum theory of superresolution for two incoherent optical point sources. Phys. Rev. X 6, 031033 (2016).

    Google Scholar 

  138. Toninelli, E. et al. Resolution-enhanced quantum imaging by centroid estimation of biphotons. Optica 6, 347–353 (2019).

    Google Scholar 

  139. Tsang, M. Quantum imaging beyond the diffraction limit by optical centroid measurements. Phys. Rev. Lett. 102, 253601 (2009).

    ADS  Google Scholar 

  140. Boto, A. N. et al. Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit. Phys. Rev. Lett. 85, 2733–2736 (2000).

    ADS  Google Scholar 

  141. D’Angelo, M., Chekhova, M. V. & Shih, Y. Two-photon diffraction and quantum lithography. Phys. Rev. Lett. 87, 013602 (2001).

    ADS  Google Scholar 

  142. Chang, H. J., Shin, H., O’Sullivan-Hale, M. N. & Boyd, R. W. Implementation of sub-Rayleigh-resolution lithography using an N-photon absorber. J. Mod. Opt. 53, 2271–2277 (2006).

    ADS  MATH  Google Scholar 

  143. Shin, H., Chan, K. W. C., Chang, H. J. & Boyd, R. W. Quantum spatial superresolution by optical centroid measurements. Phys. Rev. Lett. 107, 083603 (2011).

    ADS  Google Scholar 

  144. Rozema, L. A. et al. Scalable spatial superresolution using entangled photons. Phys. Rev. Lett. 112, 223602 (2014).

    ADS  Google Scholar 

  145. Matthews, J. C. Scalable imaging of superresolution. Physics 7, 59 (2014).

    Google Scholar 

  146. Thiel, C. et al. Quantum imaging with incoherent photons. Phys. Rev. Lett. 99, 133603 (2007).

    ADS  Google Scholar 

  147. Oppel, S., Büttner, T., Kok, P. & von Zanthier, J. Superresolving multiphoton interferences with independent light sources. Phys. Rev. Lett. 109, 233603 (2012).

    ADS  Google Scholar 

  148. Moreau, P.-A., Toninelli, E., Gregory, T. & Padgett, M. J. Ghost imaging using optical correlations. Laser Photon. Rev. 12, 1700143 (2018).

    ADS  Google Scholar 

  149. Klyshko, D. N. A simple method of preparing pure states of an optical field, of implementing the Einstein–Podolsky–Rosen experiment, and of demonstrating the complementarity principle. Sov. Phys. Uspekhi 31, 74–85 (1988).

    ADS  Google Scholar 

  150. Pittman, T. B. et al. Two-photon geometric optics. Phys. Rev. A 53, 2804–2815 (1996).

    ADS  Google Scholar 

  151. Aspden, R. S. et al. Photon-sparse microscopy: visible light imaging using infrared illumination. Optica 2, 1049–1052 (2015).

    Google Scholar 

  152. Bennink, R. S., Bentley, S. J. & Boyd, R. W. Two-photon coincidence imaging with a classical source. Phys. Rev. Lett. 89, 113601 (2002).

    ADS  Google Scholar 

  153. Gatti, A., Brambilla, E., Bache, M. & Lugiato, L. A. Ghost imaging with thermal light: comparing entanglement and classicalcorrelation. Phys. Rev. Lett. 93, 093602 (2004).

    ADS  Google Scholar 

  154. Gatti, A., Brambilla, E. & Lugiato, L. Quantum imaging. Prog. Opt. 51, 251–348 (2008).

    ADS  Google Scholar 

  155. Moreau, P.-A. et al. Resolution limits of quantum ghost imaging. Opt. Express 26, 7528–7536 (2018).

    ADS  Google Scholar 

  156. Brida, G. et al. Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light. Phys. Rev. A 83, 063807 (2011).

    ADS  Google Scholar 

  157. Baleine, E., Dogariu, A. & Agarwal, G. S. Correlated imaging with shaped spatially partially coherent light. Opt. Lett. 31, 2124–2126 (2006).

    ADS  Google Scholar 

  158. Pepe, F. V. et al. Diffraction-limited plenoptic imaging with correlated light. Phys. Rev. Lett. 119, 243602 (2017).

    ADS  Google Scholar 

  159. Altmann, Y. et al. Quantum-inspired computational imaging. Science 361, eaat2298 (2018).

    Google Scholar 

  160. Shapiro, J. H. & Boyd, R. W. The physics of ghost imaging. Quantum Inf. Process. 11, 949–993 (2012).

    MATH  Google Scholar 

  161. Genovese, M. Real applications of quantum imaging. J. Opt. 18, 073002 (2016).

    ADS  Google Scholar 

  162. Magana-Loaiza, O. S., Howland, G. A., Malik, M., Howell, J. C. & Boyd, R. W. Compressive object tracking using entangled photons. Appl. Phys. Lett. 102, 231104 (2013).

    ADS  Google Scholar 

  163. Aspden, R. S. et al. Photon-sparse microscopy: visible light imaging using infrared illumination. Optica 2, 1049–1052 (2015).

    Google Scholar 

  164. Jansen, C. et al. Terahertz imaging: applications and perspectives. Appl. Opt. 49, E48–E57 (2010).

    Google Scholar 

  165. Rubin, M. H. & Shih, Y. Resolution of ghost imaging for nondegenerate spontaneous parametric down-conversion. Phys. Rev. A 78, 033836 (2008).

  166. Chan, K. W. C., O’Sullivan, M. N. & Boyd, R. W. Two-color ghost imaging. Phys. Rev. A 79, 033808 (2009).

    ADS  Google Scholar 

  167. Denis, S., Moreau, P.-A., Devaux, F. & Lantz, E. Temporal ghost imaging with twin photons. J. Opt. 19, 034002 (2017).

    ADS  Google Scholar 

  168. Schori, A., Borodin, D., Tamasaku, K. & Shwartz, S. Ghost imaging with paired X-ray photons. Phys. Rev. A 97, 063804 (2018).

    ADS  Google Scholar 

  169. Khakimov, R. I. et al. Ghost imaging with atoms. Nature 540, 100–103 (2016).

    ADS  Google Scholar 

  170. Lemos, G. B. et al. Quantum imaging with undetected photons. Nature 512, 409–412 (2014).

    ADS  Google Scholar 

  171. Lahiri, M., Lapkiewicz, R., Lemos, G. B. & Zeilinger, A. Theory of quantum imaging with undetected photons. Phys. Rev. A 92, 013832 (2015).

  172. Zou, X. Y., Wang, L. J. & Mandel, L. Induced coherence and indistinguishability in optical interference. Phys. Rev. Lett. 67, 318–321 (1991).

    ADS  Google Scholar 

  173. Wang, L. J., Zou, X. Y. & Mandel, L. Induced coherence without induced emission. Phys. Rev. A 44, 4614–4622 (1991).

    ADS  Google Scholar 

  174. Ou, Z. Y., Wang, L. J., Zou, X.-B. & Mandel, L. Coherence in two-photon down-conversion induced by a laser. Phys. Rev. A 41, 1597–1601 (1990).

    ADS  Google Scholar 

  175. Kalashnikov, D. A., Paterova, A. V., Kulik, S. P. & Krivitsky, L. A. Infrared spectroscopy with visible light. Nat. Photon. 10, 98–101 (2016).

    ADS  Google Scholar 

  176. Hochrainer, A., Lahiri, M., Lapkiewicz, R., Lemos, G. B. & Zeilinger, A. Quantifying the momentum correlation between two light beams by detecting one. Proc. Natl Acad. Sci. USA 114, 1508–1511 (2017).

    ADS  MathSciNet  MATH  Google Scholar 

  177. Elitzur, A. C. & Vaidman, L. Quantum mechanical interaction-free measurements. Found. Phys. 23, 987–997 (1993).

    ADS  Google Scholar 

  178. Vaidman, L. On the realization of interaction-free measurements. Quantum Opt. J. Eur. Opt. Soc. B 6, 119–126 (1994).

    ADS  Google Scholar 

  179. Kwiat, P. G. Experimental and theoretical progress in interaction-free measurements. Phys. Scr. 1998, 115–121 (1998).

    Google Scholar 

  180. Vaidman, L. Are interaction-free measurements interaction free? Opt. Spectrosc. 91, 352–357 (2001).

    ADS  Google Scholar 

  181. Geszti, T. Interaction-free measurement and forward scattering. Phys. Rev. A 58, 4206–4209 (1998).

    ADS  Google Scholar 

  182. Misra, B. & Sudarshan, E. C. G. The Zeno’s paradox in quantum theory. J. Math. Phys. 18, 756–763 (1977).

    ADS  MathSciNet  Google Scholar 

  183. Kwiat, P., Weinfurter, H., Herzog, T., Zeilinger, A. & Kasevich, M. A. Interaction-free measurement. Phys. Rev. Lett. 74, 4763–4766 (1995).

    ADS  Google Scholar 

  184. Tsegaye, T. et al. Efficient interaction-free measurements in a high-finesse interferometer. Phys. Rev. A 57, 3987–3990 (1998).

    ADS  Google Scholar 

  185. Kwiat, P. G. et al. High-efficiency quantum interrogation measurements via the quantum Zeno effect. Phys. Rev. Lett. 83, 4725–4728 (1999).

    ADS  Google Scholar 

  186. White, A. G., Mitchell, J. R., Nairz, O. & Kwiat, P. G. Interaction-free imaging. Phys. Rev. A 58, 605–613 (1998).

    ADS  Google Scholar 

  187. Zhang, Y. et al. Interaction-free ghost-imaging of structured objects. Opt. Express 27, 2212–2224 (2019).

    ADS  Google Scholar 

  188. Yan, F., Iliyasu, A. M. & Le, P. Q. Quantum image processing: a review of advances in its security technologies. Int. J Quantum Inf. 15, 1730001 (2017).

    MathSciNet  MATH  Google Scholar 

  189. Di Lena, F., Pepe, F., Garuccio, A. & D'Angelo, M. Correlation plenoptic imaging: an overview. Appl. Sci. 8, 1958 (2018).

    Google Scholar 

  190. Schleich, W. P. et al. Quantum technology: from research to application. Appl. Phys. B 122, 130 (2016).

    ADS  Google Scholar 

  191. Barnett, S. M. Journeys from quantum optics to quantum technology. Prog. Quantum Electron. 54, 19–45 (2017).

    Google Scholar 

  192. Mohseni, M. Commercialize quantum technologies in five years. Nature 543, 171–175 (2017).

    Google Scholar 

  193. Lantz, E., Moreau, P.-A. & Devaux, F. Optimizing the signal-to-noise ratio in the measurement of photon pairs with detector arrays. Phys. Rev. A 90, 063811 (2014).

    ADS  Google Scholar 

  194. Tasca, D. S., Edgar, M. P., Izdebski, F., Buller, G. S. & Padgett, M. J. Optimizing the use of detector arrays for measuring intensity correlations of photon pairs. Phys. Rev. A 88, 013816 (2013).

    ADS  Google Scholar 

Download references

Acknowledgements

This work was funded by the UK Engineering and Physical Sciences Research Council (EPSRC; QuantIC EP/M01326X/1) and the European Research Council (TWISTS, 340507, grant no. 192382). P.-A.M. acknowledges the support from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie fellowship grant agreement no. 706410, of the Leverhulme Trust through the Research Project Grant ECF-2018-634 and of the Lord Kelvin/Adam Smith Leadership Fellowship scheme. E.T. acknowledges the financial support from the EPSRC Centre for Doctoral Training Intelligent Sensing and Measurement (EP/L016753/1). T.G. acknowledges the financial support from the EPSRC (EP/N509668/1) and the Professor Jim Gatheral quantum technology studentship.

Author information

Authors and Affiliations

  1. SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, UK

    Paul-Antoine Moreau, Ermes Toninelli, Thomas Gregory & Miles J. Padgett

Authors
  1. Paul-Antoine Moreau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ermes Toninelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas Gregory
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Miles J. Padgett
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

P.-A.M. and M.J.P. made substantial contributions to discussions of the content. P.-A.M., T.G. and M.J.P. researched data for the article. P.-A.M., E.T., T.G. and M.J.P. wrote the article and reviewed and/or edited the manuscript before submission.

Corresponding authors

Correspondence to Paul-Antoine Moreau or Miles J. Padgett.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Glossary

Quantum decoherence

The loss of quantum coherence of a quantum system through its interaction with the environment. This loss of coherence leads to the collapse of the system wavefunction, which leads to loose quantum superposition or entanglement.

Sub-shot-noise

A variable exhibits sub-shot-noise statistics if the noise on that variable is smaller than the shot noise. The shot noise is due to the discrete and independent arrival of photons, which exhibits Poisson statistics.

Quantum squeezing

A state is said to be squeezed if the noise of one observable measured on that state is below the symmetric Heisenberg limit; this implies that the conjugate variable noise is itself above that limit, as imposed by the Heisenberg uncertainty principle.

Field quadratures

Operators that correspond to the real and imaginary parts of the amplitude of the quantized electromagnetic field. They compose a basis for the phase space of the quantized field.

Quantum non-demolition measurement

A type of measurement of a quantum system that preserves the uncertainty of the measured observable. This implies, in particular, that the system is not destroyed by the measurement, for example, a measured photon would not be absorbed during the measurement process.

Homodyne detectors

A detector used to measure different components of the quantized electromagnetic phase space. It is based on detecting the interference occurring on the two outputs of a beam splitter that mixes a controlled bright local oscillator and the state of light that is to be measured.

Thermal light

Light whose statistic is similar to that of thermal radiation. As a result, such light is subject to super-Poissonian intensity fluctuations.

NOON states

A state composed of N particles in a superposition of being all in one mode or all in a second mode.

LiDAR systems

A system that emits light pulses and measures the time-of-flight of their echoes to assess the distance to reflecting objects. It is based on the same principle as a RADAR system but uses light instead of radio waves.

Photon anti-bunching

A property of light in which photons are more evenly spaced in time than in an ideal laser beam (coherent state). Anti-bunched light will exhibit sub-shot-noise statistics over time.

Hanbury Brown–Twiss effect

A correlation effect observed between the intensities detected by two detectors when each receive light from two independent sources. It requires the interference of two photons to occur to be explained at a quantum level.

Weak measurements

Measurements for which the measuring device is weakly coupled with the measured system. Weak measurements disturb the measured system less than conventional projective measurements.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moreau, PA., Toninelli, E., Gregory, T. et al. Imaging with quantum states of light. Nat Rev Phys 1, 367–380 (2019). https://doi.org/10.1038/s42254-019-0056-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s42254-019-0056-0

This article is cited by

Search

Advanced 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