# Encoding and decoding images in quantum optical correlations

Chloé Vernière, Baptiste Courme, Hugo Defienne

<figure><img src="image_1.png" /></figure>

To cite this version:

Chloé Vernière, Baptiste Courme, Hugo Defienne. Encoding and decoding images in quantum optical correlations. Photoniques, 2025, 131, pp.42-47. 10.1051/photon/202513142. hal-05071789

HAL Id: hal-05071789

https://hal.science/hal-05071789v1

Submitted on 17 May 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# ENCODING AND DECODING
IMAGES IN QUANTUM
OPTICAL CORRELATIONS

Chloé VERNIÈRE<fnref n="1" />, Baptiste COURME<fnref n="1" />,<fnref n="2" />, Hugo DEFIENNE<fnref n="1" />,*

<figure><img src="image_3.png" /></figure>

Quantum correlations, such as those existing between photons produced by spontaneous parametric down-conversion (SPDC), are ubiquitous in quantum photonic technologies. To develop applications, they must be precisely tailored and efficiently measured, which is often challenging in practice. This article presents an image encoding-decoding method based on the quantum correlations of photon pairs, highlighting recent advances in detecting and controlling these correlations for imaging and sensing applications.

https://doi.org/10.1051/photon/202513142

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Quantum imaging exploits non-classical optical properties to surpass the performance of classical systems or to develop new imaging modalities [1]. Building on quantum metrology and sensing, this field has developed over the past 40 years. Advances in detector and source technologies, combined with conceptual progress in quantum phenomena such as entanglement and non-locality, have gradually paved the way for practical applications. Notably, the past five years have seen the first proof-of-principle

demonstrations of quantum micros-copes employing squeezed light [2], single-photon emitters [3] and en-tangled photons [4].

Among quantum imaging tech-niques, many leverage photon correlations to enhance imaging performance. Photon correlations in so-called ‘twin beams’ were first observed in 1970 in light emitted from $\chi(2)$ nonlinear crystals [5]. Since then, this nonlinear optical process, known as spontaneous parametric down-conversion (SPDC) [6], has been extensively studied. Today, it underpins most non-classical light sources used in modern experiments

and applications, particularly those that produce entangled photon pairs.

## SPONTANEOUS PARAMETRIC DOWN CONVERSION

SPDC is a non-linear process in which a photon from a high-energy (e.g. blue) pump laser is converted into two lower-energy (e.g. infrared) pho-tons called signal and idler (Fig. 1a). It is a very inefficient process, as most of the pump photons pass through the crystal unperturbed, with only a small portion ($10^{-5}$ to $10^{-12}$) pro-ducing a pair of down-converted photons. When operating in the low gain regime, for example by using a

<footnote n="1">¹Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, F-75005 Paris</footnote>

<footnote n="2">²Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 rue Lhomond, 75005 Paris, France</footnote>

<footnote>*hugo.defienne@insp.upmc.fr</footnote>
continuous-wave pump laser with hundreds of mW intensity, the probability of generating a double-pair is negligible and the output state is well described by a two-photon state of the form

$$|\psi\rangle \approx C_0|0\rangle + C_1 \sum_{k,l} \Psi_{kl} a_k^\dagger a_l^\dagger |0\rangle, \quad (1)$$

where $C_0$ and $C_1$ are normalization coefficients ($C_0 \gg C_1$), $a_k^\dagger$ is the creation operator of a photon in the mode k of the electromagnetic field (spatial, spectral, and polarization) and $\Psi_{kl}$ is the two-photon wavefunction.

The properties of $\Psi_{kl}$ – and thus those of the quantum correlations of the photons emitted by the source – are entirely determined by the characteristics of the pump laser and the crystal used. On the one hand, engineering the crystal parameters allows modification of the phase-matching conditions (Figs. 1b and c), thereby changing the properties of the state. This is the case, for

example, when using periodically poled crystals [7]. On the other hand, one can also modify the properties of the pump laser, such as its wavelength or spatial structure. This latter approach, known as pump shaping, is particularly attractive since it allows for adaptive and dynamic control of the two-photon state. Over the past years, many research teams have

started using it to optimize their states for specific applications [8]. In this article, we describe an approach that exploits this idea to tailor the spatial correlations between photon pairs in the form of arbitrary objects.

<figure><img src="image_4.png" /><figcaption>**Figure 1.** a, Illustration of the spontaneous parametric down conversion (SPDC) process. b, Momentum and c energy conservation in SPDC.</figcaption></figure>

## ENCODING AND DECODING IMAGES

A key feature of SPDC is the transfer of the pump beam first-order spatial coherence to the down-converted photon pairs' second-order coherence. Our approach, illustrated in Figure 2a, leverages this property by placing an object and a thin nonlinear crystal at the front and back focal planes of a lens. In such a configuration, the crystal is effectively illuminated with a pump that has the shape of the transverse spatial Fourier transform of the object. Due to momentum conservation (Fig. 1b), the structure of the photon pairs spatial correlations

<figure><img src="image_5.png" /></figure>
a. Image encoding apparatus

<figure><img src="image_6.png" /></figure>

c. Correlations with focused pump

<figure><img src="image_7.png" /></figure>

**Figure 2.** a, Simplified experimental setup. A collimated blue continuous-wave diode laser (405 nm) illuminates an object, which is Fourier imaged by a lens onto a β-Barium-Borate nonlinear crystal (0.5 mm thick). The down-converted photon pairs have the same wavelength (810 nm) and polarization (perpendicular to the pump). A spectral filter after the crystal removes the pump photons. A second lens Fourier images the crystal onto a single-photon-sensitive camera, here an Electron Multiplied Charge-Coupled Device (EMCCD) camera. b, Intensity and correlation images without the object and the lens in front of the crystal. c, Intensity and correlation images with only the lens. d, Intensity and correlation images with both the lens and the object.

b. Correlations with collimated pump

<figure><img src="image_8.png" /></figure>

d. Image decoded from correlations

<figure><img src="image_9.png" /></figure>

**Figure 3.** Preliminary results obtained by replacing the EMCCD by a Tpx3cam camera in the quantum encoding-decoding image scheme described in Figure 1a. a,b et c, Correlations images of three different objects (cross, flower and standing cat) reconstructed from 10 seconds of acquisition. Direct intensity images are shown in inset.

<figure><img src="image_10.png" /></figure>
is consequently modulated. Specifically, the associated two-photon wavefunction, expressed in the momentum basis, takes exactly the form of the object:

$$ \Psi_{\mathbf{k}_{\text{ski}}} = t(\mathbf{k}_s + \mathbf{k}_i), $$

where $\mathbf{k}_s$ and $\mathbf{k}_i$ are the momenta of the signal and idler photons, respectively, and $t$ is the object. These correlations are measured by Fourier imaging the down-converted field onto a single-photon-sensitive camera and detecting coincidences between all pixel pairs [9]. Note that in our experiment, the crystal is cut to produce frequency-degenerate (810 nm) photon pairs with the same polarization (Type I SPDC).

To intuitively understand the shaping of correlations, we first consider the case without the object and lens before the crystal. The collimated pump at the crystal implies a near-zero transverse momentum ($\mathbf{k}_p \approx 0$), leading to strong anti-correlations between the signal and idler photons momenta: $\mathbf{k}_s+\mathbf{k}_i \approx 0$. Each time a photon is detected at a certain position on the camera (placed in the Fourier plane of the crystal), its twin appears in the symmetrical position. These strong anti-correlations form a sharp central peak in the measured correlation image (Fig. 2b), constructed by summing the signal and idler photon positions for each detected pair ($\mathbf{k}_s+\mathbf{k}_i$).

With the lens, the pump is focused on the crystal, broadening its transverse momentum ($\mathbf{k}_p = \Delta\mathbf{k}$, with $|\Delta\mathbf{k}| \gg 0$). Momentum conservation now gives $\mathbf{k}_s+\mathbf{k}_i = \Delta\mathbf{k}$, reducing the strength of anti-correlations and widening the correlation peak (Fig. 2c). Note that only the spatial correlations are affected - the direct intensity remains uniform.

Placing an object (e.g. a 'sleeping cat') in the back focal plane of the lens projects its Fourier transform onto the pump field at the crystal. Conversely, this means the pump field transverse spatial momentum in the crystal plane has exactly the cat shape. Momentum conservation effectively 'encodes' the cat shape into the photon pairs spatial correlations. Then, measuring coincidences in the Fourier plane 'decodes' the cat in the correlation image, while the intensity image remains uniform. Our approach enables shaping photon-pair correlations into arbitrary objects, without any information appearing in the intensity image.

## CORRELATION-BASED IMAGING

A key aspect of this approach is the ability to reconstruct correlation images by measuring photon coincidences across all camera pixel pairs. In the work presented above and reported in Ref. [10], we used an EMCCD camera, requiring 2 to 10 hours to reconstruct a high-quality correlation image, depending on the object complexity. While suitable for proof-of-principle demonstrations, this duration is impractical for real-world applications.

In recent years, new technologies have emerged, significantly accelerating this process. Among them, single photon avalanche diode (SPAD) cameras or intensified

# Ultra-cold Atoms, Ions, Molecules and Quantum Technologies

By
**Robin Kaiser,**
**Michèle Leduc,**
**Hélène Perrin**

Preface By
**Alain**
**Aspect**

Current Natural Sciences

QUANTUM INFORMATION

Robin KAISER, Michèle LEDUC and Hélène PERRIN, Eds

Ultra-Cold Atoms, Ions, Molecules and Quantum Technologies

Preface by Alain Aspect

<figure><img src="image_11.png" /></figure>

edp sciences

Science Press

The field of cold atoms was born fourty years ago and today remains a theme regularly awarded Nobel Prizes and at the forefront of physics research. This book presents the most recent developments and traces the exceptional growth of this field over the last years.

Also available in e-book format

For sale on
laboutique.edpsciences.fr

ISBN: 978-2-7598-2745-9

168 illustrated pages

Price: 95 €

<figure><img src="image_12.png" /></figure>

Prix Roberval

<figure><img src="image_13.png" /></figure>
The TPX3CAM is an advanced intensified hybrid Complementary Metal-Oxide-Semiconductor (CMOS) sensor designed for single-photon detection. This sensor is based on technology originally developed for particle detection at CERN. An optically sensitive silicon sensor is bonded to a specialized fast readout chip. This combination results in a sensor featuring 256×256 pixels, each measuring 55µm × 55µm, with exceptionally high quantum efficiency. To achieve single-photon sensitivity, the incoming signal must be amplified. This is accomplished by placing a photon intensifier in front of the sensor. The intensifier consists of a photocathode that converts the incoming light into an electron beam. This electron beam is then amplified using a multichannel plate (MCP) and subsequently converted back into photons by a scintillator. The intensifier has a quantum efficiency of 20% at 810nm. The photon flash produced during the amplifying process hits more than one pixel on the camera, but centroid algorithms resolve this by identifying the central pixel based on spatial distribution and timing. This sensor distinguishes itself from others on the market with its event-based operating mode, in contrast to the frame-based approach used by most other cameras.

The high-speed readout chip records each pixel individually, assigning a time tag to each photon that strikes the sensor with sufficient energy. Each time tag corresponds to a detection event. The detection process operates as follows: each pixel has its own electrical threshold Vth, and only pixels that exceed this threshold trigger the readout process and time measurement. The chip records the Time of Arrival (TOA) with a precision of 1.56 ns and the Time Over Threshold (TOT) with a precision of 25 ns. These two time tags are subsequently used in the centroid process, enabling single-photon sensitivity. This new technology makes it straightforward to detect temporal coincidences between photons. In post-processing, a temporal correlation window of width $\Delta T$ is applied across the entire dataset. Within this window, all pixel positions corresponding to detection events are examined. If at least two events occur within the same temporal window, the pixel positions of these events are identified and recorded. By repeating this process for all time intervals in the dataset, a spatial coincidence map is constructed. This map highlights the positions of pixels where coincident detections occurred, enabling the recovery of spatial correlations between photons with high precision.

<figure><img src="image_14.png" /><figcaption>**Figure 4.** a, Tpx3Cam camera setup configuration (the computer is not represented). b, The incoming SPDC photons interact with the intensifier resulting in a flash of photons. Those are detected by the CMOS sensor and the electronic signal is recorded by the fast readout electronics embedded in the sensor. Post processing enable the correlation measurement between the pixels.</figcaption></figure>

time-stamping cameras, such as the Tpx3Cam (see box), are extremely promising. They benefit from a much higher temporal resolution, typically 1-10 ns, higher frame rates - up to 8.10⁵ frames per second - and can operate in an event-based detection mode, which considerably simplifies output data processing. Integrated into our experiment, the Tpx3cam enables, for example, the acquisition of correlation images in under 10 seconds with quality comparable to those obtained with the EMCCD, representing a 1000-fold reduction in acquisition time.

Preliminary results obtained with this camera are shown in Figure 3.

These new camera technologies will facilitate the use of our encoding-decoding imaging scheme and gradually lead it towards potential applications. For example, promising avenues we are exploring include the possibility of transmitting images in an absolutely secure manner, bridging the fields of quantum key distribution and imaging. Another key direction is improving image transmission through complex or aberrating media, such as atmospheric

turbulence, fog, or biological tissues, where quantum light demonstrates greater robustness than classical signals.

## CONCLUSION

As seen through the example described in this paper, correlation-based quantum imaging approaches - a subcategory of optical quantum imaging and sensing schemes - represent a new form of imaging with significant potential. However, it is also evident that substantial technological efforts are still required
for these proof-of-principle experiments to transition to real-world applications and compete with classical imaging systems. Among the most critical are the limited photon detection efficiency of single-photon sensitive cameras - rarely exceeding 30% - and the inherent inefficiency of SPDC in generating correlated photons. While these limitations are still manageable when working with two-photon states, the scaling rapidly deteriorates for generating and detecting N-photon states: both photon detection efficiency and conversion probability decrease exponentially with N.

Despite its current limitations, recent progress in quantum imaging is encouraging. Alternative photon sources to SPDC, such as semiconductor quantum dots [11], are being actively developed and show promise. Simultaneously, event-based cameras with higher quantum efficiency and improved temporal resolution are advancing, often driven by consumer market demands - such as the integration of SPAD cameras in smartphones. As these technologies continue to evolve, quantum imaging remains most relevant for specialized applications, including biological imaging of photo-sensitive samples [4] and imaging in challenging wavelength ranges [12].

## REFERENCES

[1] H. Defienne, W. P. Bowen, M. Chekhova, G. B. Lemos, D. Oron, S. Ramelow, N. Treps, and D. Faccio, Nat. Photonics **18**, 1024 (2024)

[2] C. A. Casacio, L. S. Madsen, A. Terrasson, M. Waleed, K. Barnscheidt, B. Hage, M. A. Taylor, and W. P. Bowen, Nature **594**, 201 (2021)

[3] R. Tenne, U. Rossman, B. Rephael, Y. Israel, A. Krupinski-Ptaszek, R. Lapkiewicz, Y. Silberberg, and D. Oron, Nat. Photonics **13**, 116 (2019)

[4] P. Cameron, B. Courme, C. Vernière, R. Pandya, D. Faccio, and H. Defienne, Science **383**, 1142 (2024)

[5] D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. **25**, 84 (1970)

[6] C. Couteau, Contemp. Phys. **59**, 291 (2018)

[7] O. Yesharim, S. Pearl, J. Foley-Comer, I. Juwiler, and A. Arie, Sci. Adv. **9**, eade7968 (2023)

[8] A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature **412**, 313 (2001)

[9] H. Defienne, M. Reichert, and J. W. Fleischer, Phys. Rev. Lett. **120**, 203604 (2018)

[10] C. Vernière and H. Defienne, Phys. Rev. Lett. **133**, 093601 (2024)

[11] J. Loredo et al., Nat. Photonics **10**, 340 (2016)

[12] D. P. Ryan, K. Meier, K. Seitz, D. Hanson, D. Morales, D. M. Palmer, B. Hanson, P. M. Goodwin, R. Newell, R. M. Holmes, et al., Optica **11**, 1261 (2024)

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

# Discover our range of Optical Spectrum Analyzers

World-class optical performance for wellbeing, biomedical, and environmental sensing applications.

Discover it here:

<figure><img src="image_17.png" /></figure>

Our distributor in France:

<figure><img src="image_18.png" /></figure>

wavetel

a simac group company

www.wavetel.fr
about@wavetel.fr