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.

Polarization entanglement-enabled quantum holography

Abstract

Holography is a cornerstone characterization and imaging technique that can be applied to the full electromagnetic spectrum, from X-rays to radio waves or even particles such as neutrons. The key property in all these holographic approaches is coherence, which is required to extract the phase information through interference with a reference beam. Without this, holography is not possible. Here we introduce a holographic imaging approach that operates on first-order incoherent and unpolarized beams, so that no phase information can be extracted from a classical interference measurement. Instead, the holographic information is encoded in the second-order coherence of entangled states of light. Using spatial-polarization hyper-entangled photon pairs, we remotely reconstruct phase images of complex objects. Information is encoded into the polarization degree of the entangled state, allowing us to image through dynamic phase disorder and even in the presence of strong classical noise, with enhanced spatial resolution compared with classical coherent holographic systems. Beyond imaging, quantum holography quantifies hyper-entanglement distributed over 104 modes via a spatially resolved Clauser–Horne–Shimony–Holt inequality measurement, with applications in quantum state characterization.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Schematic of the quantum holographic reconstruction.
Fig. 2: Quantum holography without polarization entanglement.
Fig. 3: Experimental set-up.
Fig. 4: Quantum holography through dynamic phase disorder and in the presence of stray light.
Fig. 5: Resolution enhancement.
Fig. 6: Spatially resolved CHSH inequality violation.

Data availability

Data that support the plots within this paper and other findings of this study are available from https://doi.org/10.5525/gla.researchdata.1093. Source data are provided with this paper.

References

  1. 1.

    Gabor, D. A new microscopic principle. Nature 161, 777–778 (1948).

    ADS  Google Scholar 

  2. 2.

    Marquet, P. et al. Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy. Opt. Lett. 30, 468–470 (2005).

    ADS  Google Scholar 

  3. 3.

    Refregier, P. & Javidi, B. Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20, 767–769 (1995).

    ADS  Google Scholar 

  4. 4.

    Heanue, J. F., Bashaw, M. C. & Hesselink, L. Volume holographic storage and retrieval of digital data. Science 265, 749–752 (1994).

    ADS  Google Scholar 

  5. 5.

    Yamaguchi, I. & Zhang, T. Phase-shifting digital holography. Opt. Lett. 22, 1268–1270 (1997).

    ADS  Google Scholar 

  6. 6.

    Moreau, P.-A., Toninelli, E., Gregory, T. & Padgett, M. J. Imaging with quantum states of light. Nat. Rev. Phys. 1, 367–380 (2019).

    Google Scholar 

  7. 7.

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

    ADS  Google Scholar 

  8. 8.

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

    ADS  Google Scholar 

  9. 9.

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

    ADS  Google Scholar 

  10. 10.

    Nasr, M. B., Saleh, B. E. A., Sergienko, A. V. & Teich, M. C. Demonstration of dispersion-canceled quantum-optical coherence tomography. Phys. Rev. Lett. 91, 083601 (2003).

    ADS  Google Scholar 

  11. 11.

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

    ADS  Google Scholar 

  12. 12.

    Ono, T., Okamoto, R. & Takeuchi, S. An entanglement-enhanced microscope. Nat. Commun. 4, 2426 (2013).

    ADS  Google Scholar 

  13. 13.

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

    ADS  Google Scholar 

  14. 14.

    Abouraddy, A. F., Saleh, B. E. A., Sergienko, A. V. & Teich, M. C. Quantum holography. Opt. Express 9, 498–505 (2001).

    ADS  Google Scholar 

  15. 15.

    Asban, S., Dorfman, K. E. & Mukamel, S. Quantum phase-sensitive diffraction and imaging using entangled photons. Proc. Natl Acad. Sci. USA 116, 11673–11678 (2019).

    ADS  Google Scholar 

  16. 16.

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

    ADS  Google Scholar 

  17. 17.

    Devaux, F., Mosset, A., Bassignot, F. & Lantz, E. Quantum holography with biphotons of high Schmidt number. Phys. Rev. A 99, 033854 (2019).

    ADS  Google Scholar 

  18. 18.

    Barreiro, J. T., Langford, N. K., Peters, N. A. & Kwiat, P. G. Generation of hyperentangled photon pairs. Phys. Rev. Lett. 95, 260501 (2005).

    ADS  Google Scholar 

  19. 19.

    Hegazy, S. F. & Obayya, S. S. A. Tunable spatial–spectral phase compensation of type-I (ooe) hyperentangled photons. J. Opt. Soc. Am. B 32, 445–450 (2015).

    ADS  Google Scholar 

  20. 20.

    Defienne, H., Reichert, M. & Fleischer, J. W. General model of photon-pair detection with an image sensor. Phys. Rev. Lett. 120, 203604 (2018).

    ADS  Google Scholar 

  21. 21.

    Howell, J. C., Bennink, R. S., Bentley, S. J. & Boyd, R. W. 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 

  22. 22.

    Kwiat, P. G., Barraza-Lopez, S., Stefanov, A. & Gisin, N. Experimental entanglement distillation and ‘hidden’ non-locality. Nature 409, 1014–1017 (2001).

    ADS  Google Scholar 

  23. 23.

    Lidar, D. A. & Birgitta Whaley, K. in Irreversible Quantum Dynamics (eds Benatti, F. & Floreanini, R.) 83–120 (Lecture Notes in Physics, Springer, 2003).

  24. 24.

    Kwiat, P. G., Berglund, A. J., Altepeter, J. B. & White, A. G. Experimental verification of decoherence-free subspaces. Science 290, 498–501 (2000).

    ADS  Google Scholar 

  25. 25.

    Kielpinski, D. et al. A decoherence-free quantum memory using trapped ions. Science 291, 1013–1015 (2001).

    ADS  Google Scholar 

  26. 26.

    Viola, L. et al. Experimental realization of noiseless subsystems for quantum information processing. Science 293, 2059–2063 (2001).

    ADS  Google Scholar 

  27. 27.

    Yamamoto, T., Hayashi, K., Özdemir, S. K., Koashi, M. & Imoto, N. Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace. Nat. Photon. 2, 488–491 (2008).

    Google Scholar 

  28. 28.

    Banaszek, K., Dragan, A., Wasilewski, W. & Radzewicz, C. Experimental demonstration of entanglement-enhanced classical communication over a quantum channel with correlated noise. Phys. Rev. Lett. 92, 257901 (2004).

    ADS  Google Scholar 

  29. 29.

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

    ADS  Google Scholar 

  30. 30.

    Tan, S.-H. et al. Quantum illumination with Gaussian states. Phys. Rev. Lett. 101, 253601 (2008).

    ADS  Google Scholar 

  31. 31.

    Defienne, H., Reichert, M., Fleischer, J. W. & Faccio, D. Quantum image distillation. Sci. Adv. 5, eaax0307 (2019).

    ADS  Google Scholar 

  32. 32.

    Gregory, T., Moreau, P.-A., Toninelli, E. & Padgett, M. J. Imaging through noise with quantum illumination. Sci. Adv. 6, eaay2652 (2020).

    ADS  Google Scholar 

  33. 33.

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

    ADS  Google Scholar 

  34. 34.

    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 

  35. 35.

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

    ADS  Google Scholar 

  36. 36.

    Glauber, R. J. The quantum theory of optical coherence. Phys. Rev. 130, 2529 (1963).

    ADS  MathSciNet  Google Scholar 

  37. 37.

    Goodman, J. W. Introduction to Fourier Optics (Roberts and Company Publishers, 2005).

  38. 38.

    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 

  39. 39.

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

    ADS  Google Scholar 

  40. 40.

    Lee, K. et al. Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications. Sensors 13, 4170–4191 (2013).

    ADS  Google Scholar 

  41. 41.

    Wang, J., Dong, L., Chen, H. & Huang, S. Birefringence measurement of biological tissue based on polarization-sensitive digital holographic microscopy. Appl. Phys. B 124, 240 (2018).

    ADS  Google Scholar 

  42. 42.

    Pircher, M. et al. Imaging of polarization properties of human retina in vivo with phase resolved transversal PS-OCT. Opt. Express 12, 5940–5951 (2004).

    ADS  Google Scholar 

  43. 43.

    Götzinger, E., Pircher, M., Sticker, M., Fercher, A. F. & Hitzenberger, C. K. Measurement and imaging of birefringent properties of the human cornea with phase-resolved, polarization-sensitive optical coherence tomography. J. Biomed. Opt. 9, 94–103 (2004).

    ADS  Google Scholar 

  44. 44.

    Allen, R. D. & David, G. B. The Zeiss–Nomarski differential interference equipment for transmitted-light microscopy. Z. Wissen. Mikrosk. Mikroskop. Tech. 69, 193–221 (1969).

    Google Scholar 

  45. 45.

    Terborg, R. A., Pello, J., Mannelli, I., Torres, J. P. & Pruneri, V. Ultrasensitive interferometric on-chip microscopy of transparent objects. Sci. Adv. 2, e1600077 (2016).

    ADS  Google Scholar 

  46. 46.

    Madan, I. et al. Holographic imaging of electromagnetic fields via electron–light quantum interference. Sci. Adv. 5, eaav8358 (2019).

    ADS  Google Scholar 

  47. 47.

    Erhard, M., Krenn, M. & Zeilinger, A. Advances in high-dimensional quantum entanglement. Nat. Rev. Phys. 2, 365–381 (2020).

    Google Scholar 

  48. 48.

    Barreiro, J. T., Wei, T.-C. & Kwiat, P. G. Beating the channel capacity limit for linear photonic superdense coding. Nat. Phys. 4, 282–286 (2008).

    Google Scholar 

  49. 49.

    Graham, T. M., Bernstein, H. J., Wei, T.-C., Junge, M. & Kwiat, P. G. Superdense teleportation using hyperentangled photons. Nat. Commun. 6, 7185 (2015).

    ADS  Google Scholar 

  50. 50.

    Deng, F.-G., Ren, B.-C. & Li, X.-H. Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. 62, 46–68 (2017).

    Google Scholar 

  51. 51.

    Barbieri, M., Cinelli, C., Mataloni, P. & De Martini, F. Polarization-momentum hyperentangled states: realization and characterization. Phys. Rev. A 72, 052110 (2005).

    ADS  Google Scholar 

  52. 52.

    Krenn, M. et al. Generation and confirmation of a (100 × 100)-dimensional entangled quantum system. Proc. Natl Acad. Sci. USA 111, 6243–6247 (2014).

    ADS  Google Scholar 

  53. 53.

    Lubin, G. et al. Quantum correlation measurement with single photon avalanche diode arrays. Opt. Express 27, 32863–32882 (2019).

    ADS  Google Scholar 

  54. 54.

    Ndagano, B. et al. Imaging and certifying high-dimensional entanglement with a single-photon avalanche diode camera. npj Quantum Inf. 6, 94 (2020).

    ADS  Google Scholar 

  55. 55.

    Reichert, M., Defienne, H. & Fleischer, J. W. Optimizing the signal-to-noise ratio of biphoton distribution measurements. Phys. Rev. A 98, 013841 (2018).

    ADS  Google Scholar 

  56. 56.

    Gonzalez, R. C. & Wintz, P. Digital Image Processing (Applied Mathematics and Computation) (Addison-Wesley, 1977).

  57. 57.

    Jha, A. K. & Boyd, R. W. Spatial two-photon coherence of the entangled field produced by down-conversion using a partially spatially coherent pump beam. Phys. Rev. A 81, 013828 (2010).

    ADS  Google Scholar 

  58. 58.

    Kulkarni, G., Subrahmanyam, V. & Jha, A. K. Intrinsic upper bound on two-qubit polarization entanglement predetermined by pump polarization correlations in parametric down-conversion. Phys. Rev. A 93, 063842 (2016).

    ADS  Google Scholar 

  59. 59.

    Kulkarni, G., Kumar, P. & Jha, A. K. Transfer of temporal coherence in parametric down-conversion. J. Opt. Soc. Am. B 34, 1637–1643 (2017).

    ADS  Google Scholar 

  60. 60.

    Mukhopadhyay, S., Sarkar, S., Bhattacharya, K. & Hazra, L. Polarization phase shifting interferometric technique for phase calibration of a reflective phase spatial light modulator. Opt. Eng. 52, 035602 (2013).

    ADS  Google Scholar 

  61. 61.

    Defienne, H., Reichert, M. & Fleischer, J. W. Adaptive quantum optics with spatially entangled photon pairs. Phys. Rev. Lett. 121, 233601 (2018).

    ADS  Google Scholar 

  62. 62.

    Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969).

    ADS  MATH  Google Scholar 

Download references

Acknowledgements

We thank M. Barbieri for stimulating discussions and useful feedback. D.F. acknowledges financial support from the Royal Academy of Engineering Chair in Emerging Technology, UK Engineering and Physical Sciences Research Council (grant nos. EP/T00097X/1 and EP/R030081/1) and from the European Union’s Horizon 2020 research and innovation programme under grant no. 801060. H.D. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant no. 840958.

Author information

Affiliations

Authors

Contributions

H.D. conceived the original idea, designed and performed the experiment, and analysed the data. H.D., A.L., B.N. and D.F. contributed to the interpretation of the results and manuscript. H.D. prepared the manuscript. D.F. supervised the project.

Corresponding authors

Correspondence to Hugo Defienne or Daniele Faccio.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Alice Meda and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Extended data

Extended Data Fig. 1 Resolution enhancement characterisation.

a and b, Experimental apparatus used for spatial frequency cut-off measurement of the quantum and classical holographic systems, respectively. c, 26 pixels period phase grating programmed on the SLM (only Alice SLM in the quantum case). d, Intensity image measured with the classical system. Inset is a zoom on the first-order diffraction peak. White dashed lines represent the edges of the aperture. e, Intensity image measured in the quantum system. f, Projection of the intensity correlation matrix onto the minus-coordinate axis r1 − r2 that shows three diffraction peaks. Inset is a zoom on the first-order diffraction peak. g, 16 pixel-period-phase grating programmed on the SLM. h, Intensity image measured with the classical system. First-order diffraction peaks are blocked by the aperture. i, Intensity image measured in the quantum system. j, Projection of the intensity correlation matrix onto r1 − r2 that still shows three diffraction peaks.

Source data

Extended Data Fig. 2 Intensity correlation images measured by Alice and Bob for 16 combinations of phase values θA and θB.

Intensity correlation images are shown by pair, with a red outline for Alice and a blue outline for Bob. Each row corresponds to a measurement setting on Alice SLM θA = {π/4, 3π/4, 5π/4, 7π/4} and each column to a measurement setting of Bob SLM θB = {0, π/2, π, 3π/2}.

Source data

Extended Data Fig. 3 Quantum holographic imaging of real objects.

a, Intensity images measured by Alice showing a piece of transparent scotch tape. b, Intensity image measured by Bob. c, Phase image reconstructed by Bob with SNR = 14. d, Amplitude image reconstructed by Bob from the same set of intensity correlation images by replacing the argument in equation (1) of the article with an absolute value. e, Intensity image measured by Alice showing parts of a bird feather. f, Intensity image measured by Bob. g, Phase image reconstructed by Bob with SNR = 13. h, Amplitude image reconstructed by Bob. 107 frames were acquired in total for each case. The white scale bar corresponds to 1mm. Phase and amplitude images retrieved by Bob are rotated by 180 degrees for convenience.

Source data

Extended Data Fig. 4 Quantum holography of non-polarisation sensitive objects.

a, Modified quantum holographic set-up to achieve phase imaging of non-polarisation sensitive phase object. The sample is inserted in a conjugate image plane of Alice SLM located between f3 and f4. Two Savart plates are inserted on each side of the sample and are slightly tilted. The sample is a microscopic slide covered by a layer of silicone adhesive generated using a spay, that effectively produces a random phase layer. b, Flat phase pattern on Alice SLM (not in use in this configuration), c and d, Intensity images measured by Alice and Bob without the Savart plates. e, Phase reconstructed by Bob using the quantum holographic approach without the Savart plates with SNR = 17. f and g, Intensity images measured by Alice and Bob with the Savart plates. h, Phase reconstructed by Bob using the quantum holographic approach with the Savart plates with SNR = 12. Each phase image was reconstructed from 5.106 frames.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. A–O and discussions.

Source data

Source Data Fig. 1

Raw data of the images shown in the figure (each table corresponds to a subfigure).

Source Data Fig. 2

Raw data of the images shown in the figure (each table corresponds to a subfigure).

Source Data Fig. 4

Raw data of the images shown in the figure (each table corresponds to a subfigure).

Source Data Fig. 5

Raw data of the plot and images shown in the figure (each table corresponds to a subfigure).

Source Data Fig. 6

Raw data of the images shown in the figure (each table corresponds to a subfigure).

Source Data Extended Data Fig. 1

Raw data of the images shown in the figure (each table corresponds to a subfigure).

Source Data Extended Data Fig. 2

Raw data of the images shown in the figure (each table corresponds to a subfigure).

Source Data Extended Data Fig. 3

Raw data of the images shown in the figure (each table corresponds to a subfigure).

Source Data Extended Data Fig. 4

Raw data of the images shown in the figure (each table corresponds to a subfigure).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Defienne, H., Ndagano, B., Lyons, A. et al. Polarization entanglement-enabled quantum holography. Nat. Phys. 17, 591–597 (2021). https://doi.org/10.1038/s41567-020-01156-1

Download citation

Further reading

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