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Polarization entanglement-enabled quantum holography


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.

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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 Source data are provided with this paper.


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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




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.

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Competing interests

The authors declare no competing interests.

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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).

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Defienne, H., Ndagano, B., Lyons, A. et al. Polarization entanglement-enabled quantum holography. Nat. Phys. 17, 591–597 (2021).

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