Resolution of Quantum Imaging with Undetected Photons

Jorge Fuenzalida; Armin Hochrainer; Gabriela Barreto Lemos; Evelyn A. Ortega; Radek Lapkiewicz; Mayukh Lahiri; Anton Zeilinger

doi:10.22331/q-2022-02-09-646

Resolution of Quantum Imaging with Undetected Photons

Jorge Fuenzalida^1,2, Armin Hochrainer^1,2, Gabriela Barreto Lemos^3,4, Evelyn A. Ortega^1,2, Radek Lapkiewicz⁵, Mayukh Lahiri⁶, and Anton Zeilinger^1,2

¹Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria
²Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, Boltzmanngasse 5, University of Vienna, Vienna A-1090, Austria
³Instituto de Física, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Rio de Janeiro, CP: 68528, Brazil
⁴Physics Department, University of Massachusetts Boston, 100 Morrissey Boulevard, Boston MA 02125, USA
⁵Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, Warsaw 02-093, Poland
⁶Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA

Published:	2022-02-09, volume 6, page 646
Eprint:	arXiv:2010.07712v2
Doi:	https://doi.org/10.22331/q-2022-02-09-646
Citation:	Quantum 6, 646 (2022).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Quantum imaging with undetected photons is a recently introduced technique that goes significantly beyond what was previously possible. In this technique, images are formed without detecting the light that interacted with the object that is imaged. Given this unique advantage over the existing imaging schemes, it is now of utmost importance to understand its resolution limits, in particular what governs the maximal achievable spatial resolution.
We show both theoretically and experimentally that the momentum correlation between the detected and undetected photons governs the spatial resolution — a stronger correlation results in a higher resolution. In our experiment, the momentum correlation plays the dominating role in determining the resolution compared to the effect of diffraction. We find that the resolution is determined by the wavelength of the undetected light rather than the wavelength of the detected light. Our results thus show that it is in principle possible to obtain resolution characterized by a wavelength much shorter than the detected wavelength.

Popular summary

Superposition and entanglement are some unique features of quantum physics. Based on these fascinating properties, new promising technologies are being developed in communications, computing, and sensing. In quantum imaging, a technique called ‘quantum imaging with undetected photons’ allows imaging an object without detecting the light that interacts with it. Therefore, this technique removes detection constraints for exotic wavelengths, enabling hyperspectral imaging and beyond possible. Although this technique was introduced in 2014, no thorough work has been done on its resolution. Here we present a comprehensive study on the resolution of quantum imaging with undetected photons.

► BibTeX data

@article{Fuenzalida2022resolutionofquantum,
  doi = {10.22331/q-2022-02-09-646},
  url = {https://doi.org/10.22331/q-2022-02-09-646},
  title = {Resolution of {Q}uantum {I}maging with {U}ndetected {P}hotons},
  author = {Fuenzalida, Jorge and Hochrainer, Armin and Lemos, Gabriela Barreto and Ortega, Evelyn A. and Lapkiewicz, Radek and Lahiri, Mayukh and Zeilinger, Anton},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {646},
  month = feb,
  year = {2022}
}

► References

[1] C. Bruschini, H. Homulle, I. M. Antolovic, S. Burri, and E. Charbon, ``Single-photon avalanche diode imagers in biophotonics: review and outlook'' Light Sci. Appl. 8, 87 (2019).
https://doi.org/10.1038/s41377-019-0191-5

[2] G. Lubin, R. Tenne, I. M. Antolovic, E. Charbon, C. Bruschini, and D. Oron, ``Quantum correlation measurement with single photon avalanche diode arrays'' Opt. Express 27, 32863–32882 (2019).
https://doi.org/10.1364/OE.27.032863

[3] A. Nomerotski ``Imaging and time stamping of photons with nanosecond resolution in Timepix based optical cameras'' Nucl. Instrum. Methods Phys. Res., Sect. A 937, 26–30 (2019).
https://doi.org/10.1016/j.nima.2019.05.034

[4] A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, ``Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions'' Phys. Rev. A 56, 3214–3225 (1997).
https://doi.org/10.1103/PhysRevA.56.3214

[5] A. Mosset, F. Devaux, and E. Lantz, ``Spatially Noiseless Optical Amplification of Images'' Phys. Rev. Lett. 94, 223603 (2005).
https://doi.org/10.1103/PhysRevLett.94.223603

[6] S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, ``Spatial correlations in parametric down-conversion'' Phys. Rep. 495, 87–139 (2010).
https://doi.org/10.1016/j.physrep.2010.06.003

[7] P. A. Moreau, E. Toninelli, T. Gregory, and M. J. Padgett, ``Imaging with quantum states of light'' Nat. Rev. Phys. 1, 367–380 (2019).
https://doi.org/10.1038/s42254-019-0056-0

[8] M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, ``Terahertz quantum sensing'' Sci. Adv. 6, eaaz8065 (2020).
https://doi.org/10.1126/sciadv.aaz8065

[9] R. Nairand M. Tsang ``Far-Field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit'' Phys. Rev. Lett. 117, 190801 (2016).
https://doi.org/10.1103/PhysRevLett.117.190801

[10] M. Parniak, S. Borówka, K. Boroszko, W. Wasilewski, K. Banaszek, and R. Demkowicz-Dobrza ński, ``Beating the Rayleigh Limit Using Two-Photon Interference'' Phys. Rev. Lett. 121, 250503 (2018).
https://doi.org/10.1103/PhysRevLett.121.250503

[11] O. S. Magaña-Loaizaand R. W. Boyd ``Quantum imaging and information'' Rep. Prog. Phys. 82, 124401 (2019).
https://doi.org/10.1088/1361-6633/ab5005

[12] G. Brida, M. Genovese, and I. R. Berchera, ``Experimental realization of sub-shot-noise quantum imaging'' Nat. Photon. 4, 227–230 (2010).
https://doi.org/10.1038/nphoton.2010.29

[13] J. Sabines-Chesterking, A. R. McMillan, P. A. Moreau, S. K. Joshi, S. Knauer, E. Johnston, J. G. Rarity, and J. C. F. Matthews, ``Twin-beam sub-shot-noise raster-scanning microscope'' Opt. Express 27, 30810–30818 (2019).
https://doi.org/10.1364/OE.27.030810

[14] G. T. Garces, H. M. Chrzanowski, S. Daryanoosh, V. Thiel, A. L. Marchant, R. B. Patel, P. C. Humphreys, A. Datta, and I. A. Walmsley, ``Quantum-enhanced stimulated emission detection for label-free microscopy'' Appl. Phys. Lett. 117, 024002 (2020).
https://doi.org/10.1063/5.0009681

[15] O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, ``Superresolution microscopy with quantum emitters'' Nano Lett. 13, 5832–5836 (2013).
https://doi.org/10.1021/nl402552m

[16] A. Classen, J. von Zanthier, M. O. Scully, and G. S. Agarwal, ``Superresolution via structured illumination quantum correlation microscopy'' Optica 4, 580–587 (2017).
https://doi.org/10.1364/OPTICA.4.000580

[17] M. Unternährer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, ``Super-resolution quantum imaging at the Heisenberg limit'' Optica 5, 1150–1154 (2018).
https://doi.org/10.1364/OPTICA.5.001150

[18] R. Tenne, U. Rossman, B. Rephael, Y. Israel, A. Krupinski-Ptaszek, R. Lapkiewicz, Y. Silberberg, and D. Oron, ``Super-resolution enhancement by quantum image scanning microscopy'' Nat. Photon. 13, 116–122 (2019).
https://doi.org/10.1038/s41566-018-0324-z

[19] D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, ``Observation of two-photon “ghost” interference and diffraction'' Phys. Rev. Lett. 74, 3600 (1995).
https://doi.org/10.1103/PhysRevLett.74.3600

[20] T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, ``Optical imaging by means of two-photon quantum entanglement'' Phys. Rev. A 52, R3429 (1995).
https://doi.org/10.1103/PhysRevA.52.R3429

[21] R. S. Bennink, S. J. Bentley, and R. W. Boyd, ``“Two-photon” coincidence imaging with a classical source'' Phys. Rev. Lett. 89, 113601 (2002).
https://doi.org/10.1103/PhysRevLett.89.113601

[22] A. Gatti, E. Brambilla, and L. Lugiato, ``Quantum imaging'' Progress in Optics 51, 251–348 (2008).
https://doi.org/10.1016/S0079-6638(07)51005-X

[23] R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, ``EPR-based ghost imaging using a single-photon-sensitive camera'' New J. Phys. 15, 073032 (2013).
https://doi.org/10.1088/1367-2630/15/7/073032

[24] G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, ``Quantum imaging with undetected photons'' Nature 512, 409–412 (2014).
https://doi.org/10.1038/nature13586

[25] M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, ``Theory of quantum imaging with undetected photons'' Phys. Rev. A 92, 013832 (2015).
https://doi.org/10.1103/PhysRevA.92.013832

[26] G. B. Lemos, V. Borish, S. Ramelow, R. Lapkiewicz, G. D. Cole, and A. Zeilinger, ``Quantum Imaging with Undetected Photons'' US Patent 9,557.262 B2; EP Patent 2 887 137 B1.

[27] D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, ``Infrared spectroscopy with visible light'' Nat. Photon. 10, 98–101 (2016).
https://doi.org/10.1038/nphoton.2015.252

[28] A. Vallés, G. Jiménez, L. J. Salazar-Serrano, and J. P. Torres, ``Optical sectioning in induced coherence tomography with frequency-entangled photons'' Phys. Rev. A 97, 023824 (2018).
https://doi.org/10.1103/PhysRevA.97.023824

[29] A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, ``Tunable optical coherence tomography in the infrared range using visible photons'' Quantum Sci. Technol. 3, 025008 (2018).
https://doi.org/10.1088/2058-9565/aab567

[30] X. Y. Zou, L. J. Wang, and L. Mandel, ``Induced coherence and indistinguishability in optical interference'' Phys. Rev. Lett. 67, 318 (1991).
https://doi.org/10.1103/PhysRevLett.67.318

[31] L. J. Wang, X. Y. Zou, and L. Mandel, ``Induced coherence without induced emission'' Phys. Rev. A 44, 4614 (1991).
https://doi.org/10.1103/PhysRevA.44.4614

[32] R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, ``Quantum and Classical Coincidence Imaging'' Phys. Rev. Lett. 92, 033601 (2004).
https://doi.org/10.1103/PhysRevLett.92.033601

[33] K. W. C. Chan, M. N. O'Sullivan, and R. W. Boyd, ``Two-color ghost imaging'' Phys. Rev. A 79, 033808 (2009).
https://doi.org/10.1103/PhysRevA.79.033808

[34] P. A. Moreau, E. Toninelli, P. A. Morris, R. S. Aspden, T. Gregory, G. Spalding, R. W. Boyd, and M. J. Padgett, ``Resolution limits of quantum ghost imaging'' Opt. Express 26, 7528–7536 (2018).
https://doi.org/10.1364/OE.26.007528

[35] A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, ``Quantifying the momentum correlation between two light beams by detecting one'' Proc. Natl. Acad. Sci. USA 114, 1508–1511 (2017).
https://doi.org/10.1073/pnas.1620979114

[36] M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, ``Twin-photon correlations in single-photon interference'' Phys. Rev. A 96, 013822 (2017).
https://doi.org/10.1103/PhysRevA.96.013822

[37] H. M. Wisemanand K. Mølmer ``Induced coherence with and without induced emission'' Phys. Lett. A 270, 245–248 (2000).
https://doi.org/10.1016/S0375-9601(00)00314-5

[38] M. Lahiri, A. Hochrainer, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, ``Nonclassicality of induced coherence without induced emission'' Phys. Rev. A 100, 053839 (2019).
https://doi.org/10.1103/PhysRevA.100.053839

[39] C. H. Monken, P. H. S. Ribeiro, and S. Pádua, ``Transfer of angular spectrum and image formation in spontaneous parametric down-conversion'' Phys. Rev. A 57, 3123 (1998).
https://doi.org/10.1103/PhysRevA.57.3123

[40] A. A. Harmsand A. Zeilinger ``A new formulation of total unsharpness in radiography'' Phys. Med. Biol. 22, 70 (1977).
https://doi.org/10.1088/0031-9155/22/1/009

[41] G. D. Boreman ``Modulation transfer function in optical and electro-optical systems'' SPIE press Bellingham, WA (2001).

[42] M. Bornand E. Wolf ``Principles of optics'' Cambridge University Press (1999).

[43] J. W. Goodman ``Introduction to Fourier optics'' Roberts Company Publishers (2005).

[44] A. Schori, C. Bömer, D. Borodin, S. P. Collins, B. Detlefs, M. M. Sala, S. Yudovich, and S. Shwartz, ``Parametric down-conversion of x rays into the optical regime'' Phys. Rev. Lett. 119, 253902 (2017).
https://doi.org/10.1103/PhysRevLett.119.253902

[45] A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, ``Hyperspectral infrared microscopy with visible light'' Sci. Adv. 6, eabd0460 (2020).
https://doi.org/10.1126/sciadv.abd0460

[46] I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, ``Microscopy with undetected photons in the mid-infrared'' Sci. Adv. 6, eabd0264 (2020).
https://doi.org/10.1126/sciadv.abd0264

[47] A. V. Paterova, H. Yang, Z. S. D. Toa, and L. A. Krivitsky, ``Quantum imaging for the semiconductor industry'' Appl. Phys. Lett. 117, 054004 (2020).
https://doi.org/10.1063/5.0015614

[48] A. V. Paterova, D. A. Kalashnikov, E. Khaidarov, H. Yang, T. W. W. Mass, R. Paniagua-Domı́nguez, A. I. Kuznetsov, and L. A. Krivitsky, ``Non-linear interferometry with infrared metasurfaces'' Nanophotonics 10, 1775–1784 (2021).
https://doi.org/10.1515/nanoph-2021-0011

[49] M. Gilaberte Basset, A. Hochrainer, S. Töpfer, F. Riexinger, P. Bickert, J. R. León-Torres, F. Steinlechner, and M. Gräfe, ``Video-Rate Imaging with Undetected Photons'' Laser Photonics Rev. 15, 2000327 (2021).
https://doi.org/10.1002/lpor.202000327

Cited by

[1] Mayukh Lahiri, Balakrishnan Viswanathan, and Gabriela Barreto Lemos, Frontiers in Optics + Laser Science 2022 (FIO, LS) FM3B.6 (2022) ISBN:978-1-957171-17-3.

[2] Andres Vega, Elkin A. Santos, Jorge Fuenzalida, Marta Gilaberte Basset, Thomas Pertsch, Markus Gräfe, Sina Saravi, and Frank Setzpfandt, "Fundamental resolution limit of quantum imaging with undetected photons", Physical Review Research 4 3, 033252 (2022).

[3] Nathan R. Gemmell, Jefferson Flórez, Emma Pearce, Olaf Czerwinski, Chris C. Phillips, Rupert F. Oulton, and Alex S. Clark, "Loss-Compensated and Enhanced Midinfrared Interaction-Free Sensing with Undetected Photons", Physical Review Applied 19 5, 054019 (2023).

[4] Weiru Fan, Gewei Qian, Yutong Wang, Chen-Ran Xu, Ziyang Chen, Xun Liu, Wei Li, Xu Liu, Feng Liu, Xingqi Xu, Da-Wei Wang, and Vladislav V. Yakovlev, "Deep learning enhanced quantum holography with undetected photons", PhotoniX 5 1, 40 (2024).

[5] Jonathan Brewer, Milad Almasian, Alireza Saberigarakani, Xinyuan Zhang, Fenghua Shi, and Yichen Ding, "Resolution enhancement by subpixel sampling and computational reconstruction", Optics Letters 50 7, 2457 (2025).

[6] Sebastian Töpfer, Sergio Tovar-Perez, Josué R. León Torres, Daniel Derr, Enno Giese, Jorge Fuenzalida, and Markus Gräfe, "Synthetic quantum holography with undetected light", Optica Quantum 3 2, 129 (2025).

[7] Charles Roques-Carmes, Aviv Karnieli, David A. B. Miller, and Shanhui Fan, "Automated Modal Analysis of Entanglement with Bipartite Self-Configuring Optics", ACS Photonics 12 6, 3285 (2025).

[8] Evelyn A. Ortega, Jorge Fuenzalida, Mirela Selimovic, Krishna Dovzhik, Lukas Achatz, Sören Wengerowsky, Rodrigo F. Shiozaki, Sebastian Philipp Neumann, Martin Bohmann, and Rupert Ursin, "Spatial and spectral characterization of photon pairs at telecommunication wavelengths from type-0 spontaneous parametric downconversion", Journal of the Optical Society of America B 40 1, 165 (2023).

[9] Gewei Qian, Xingqi Xu, Shun-An Zhu, Chenran Xu, Fei Gao, V. V. Yakovlev, Xu Liu, Shi-Yao Zhu, and Da-Wei Wang, "Quantum Induced Coherence Light Detection and Ranging", Physical Review Letters 131 3, 033603 (2023).

[10] Marlon Placke, Chiara Lindner, Felix Mann, Inna Kviatkovsky, Helen M. Chrzanowski, Hendrik Bartolomaeus, Frank Kühnemann, and Sven Ramelow, "Mid-IR hyperspectral imaging with undetected photons", Optica 13 2, 328 (2026).

[11] Zheshen Zhang, Chenglong You, Omar S. Magaña-Loaiza, Robert Fickler, Roberto de J. León-Montiel, Juan P. Torres, Travis S. Humble, Shuai Liu, Yi Xia, and Quntao Zhuang, "Entanglement-based quantum information technology: a tutorial", Advances in Optics and Photonics 16 1, 60 (2024).

[12] Marta Gilaberte Basset, René Sondenheimer, Jorge Fuenzalida, Andres Vega, Sebastian Töpfer, Elkin A. Santos, Sina Saravi, Frank Setzpfandt, Fabian Steinlechner, and Markus Gräfe, "Experimental analysis of image resolution of quantum imaging with undetected light through position correlations", Physical Review A 108 5, 052610 (2023).

[13] Felix Riexinger, Mirco Kutas, Björn Haase, Michael Bortz, and Georg von Freymann, "General Simulation Method for Quantum‐Sensing Systems", Laser & Photonics Reviews 17 6, 2200945 (2023).

[14] Cherrie S. J. Lee, Andrius Zukauskas, and Carlota Canalias, "Large-aperture periodically poled Rb-doped KTP with a short-period via coercive field engineering", Optical Materials Express 13 8, 2203 (2023).

[15] Emma Pearce, Osian Wolley, Simon P. Mekhail, Thomas Gregory, Nathan R. Gemmell, Rupert F. Oulton, Alex S. Clark, Chris C. Phillips, and Miles J. Padgett, "Single-frame transmission and phase imaging using off-axis holography with undetected photons", Scientific Reports 14 1, 16008 (2024).

[16] Isaac Nape, Bereneice Sephton, Pedro Ornelas, Chane Moodley, and Andrew Forbes, "Quantum structured light in high dimensions", APL Photonics 8 5, 051101 (2023).

[17] Josué R. León-Torres, Filip Krajinić, Mohit Kumar, Marta Gilaberte Basset, Frank Setzpfandt, Valerio Flavio Gili, Branislav Jelenković, and Markus Gräfe, "Off-axis holographic imaging with undetected light", Optics Express 32 20, 35449 (2024).

[18] Mahtab Amooei, Girish Kulkarni, Jeremy Upham, and Robert W. Boyd, "Efficient characterization of spatial Schmidt modes of multiphoton entangled states produced from high-gain parametric down-conversion", Physical Review A 111 2, 023714 (2025).

[19] Xinyi Li, Shi-Hai Wei, Tianyi Chen, Mingxuan Chen, Jianing Zhou, Xueying Zhang, Si Shen, Hui Cao, Bo Jing, Guangwei Deng, and Hai-Zhi Song, "Bio-imaging with quantum twinned photons", Applied Physics Reviews 12 4, 041303 (2025).

[20] Danbi Kim, Jiho Park, Changhoon Baek, Sun Kyung Lee, and Han Seb Moon, "Complementarity of which-path information in induced and stimulated coherences via four-wave mixing process from warm Rb atomic ensemble", Optica Quantum 2 4, 288 (2024).

[21] Mirco Kutas, Björn Erik Haase, Felix Riexinger, Joshua Hennig, Patricia Bickert, Tobias Pfeiffer, Michael Bortz, Daniel Molter, and Georg von Freymann, "Quantum Sensing with Extreme Light", Advanced Quantum Technologies 5 6, 2100164 (2022).

[22] Hugo Defienne, Warwick P. Bowen, Maria Chekhova, Gabriela Barreto Lemos, Dan Oron, Sven Ramelow, Nicolas Treps, and Daniele Faccio, "Advances in quantum imaging", Nature Photonics 18 10, 1024 (2024).

[23] W. P. Bowen, Helen M. Chrzanowski, Dan Oron, Sven Ramelow, Dmitry Tabakaev, Alex Terrasson, and Rob Thew, "Quantum light microscopy", Contemporary Physics 64 3, 169 (2023).

[24] Felix Riexinger, Mirco Kutas, Björn Haase, Patricia Bickert, Daniel Molter, Michael Bortz, and Georg von Freymann, "General simulation method for spontaneous parametric down- and parametric up-conversion experiments", SciPost Physics Core 6 1, 022 (2023).

[25] Emma Pearce, Nathan R. Gemmell, Jefferson Flórez, Jiaye Ding, Rupert F. Oulton, Alex S. Clark, and Chris C. Phillips, "Practical quantum imaging with undetected photons", Optics Continuum 2 11, 2386 (2023).

[26] Siddhant Vernekar and Jolly Xavier, "Quantum Correlation Enhanced Optical Imaging", Quantum Beam Science 8 3, 19 (2024).

[27] Armin Hochrainer, Mayukh Lahiri, Manuel Erhard, Mario Krenn, and Anton Zeilinger, "Quantum indistinguishability by path identity and with undetected photons", Reviews of Modern Physics 94 2, 025007 (2022).

[28] Chieh Tsao, Haonan Ling, Alex Hinkle, Yifan Chen, Keshav Kumar Jha, Zhen-Li Yan, and Hendrik Utzat, "Enhancing spectroscopy and microscopy with emerging methods in photon correlation and quantum illumination", Nature Nanotechnology 20 8, 1001 (2025).

[29] Duncan P. Ryan and James H. Werner, "A review of quantum imaging methods and enabling technologies", Materials Today Quantum 6, 100044 (2025).

[30] Jorge Fuenzalida, Enno Giese, and Markus Gräfe, "Nonlinear Interferometry: A New Approach for Imaging and Sensing", Advanced Quantum Technologies 7 6, 2300353 (2024).

[31] Preetisha Goswami, Marta Gilaberte Basset, Jorge Fuenzalida, Markus Gräfe, and Valerio Flavio Gili, Quantum 2.0 Conference and Exhibition QW3A.2 (2024) ISBN:978-1-55752-518-5.

[32] Carsten Pitsch, Alessia Suprano, Benjamin Guery, Francesco Poggiali, Chiara Michelini, Henri Haka, Davide Moschella, Dominik Walter, Ugo Zanforlin, Massimiliano Proietti, Massimiliano Dispenza, Alberto Tosi, and Federica Villa, "Toward video-rate quantum ghost imaging", APL Photonics 10 10, 100801 (2025).

[33] Pengcheng FU, Yanzhi ZHANG, Xingqi XU, Xu LIU, Huizhu HU, and Han CAI, "Spectroscopy and imaging with quantum light", Acta Physica Sinica 75 10, 100601 (2026).

[34] Josué R. León‐Torres, Vasile‐Laurențiu Dosan, Marija M. Ćurčić, Alek Lagarrigue, Frank Setzpfandt, Markus Gräfe, and Valerio Flavio Gili, "Mid‐Infrared Quantum Scanning Microscopy via Visible Light Beyond Spatial Correlations", Laser & Photonics Reviews 20 9, e02356 (2026).

[35] Filip Krajinić, Marija Ćurčić, Marina Lekić, and Branislav Jelenković, "Characterization of tunable mid-infrared spontaneous parametric down-conversion in AgGaS2", Applied Physics B 132 4, 48 (2026).

[36] Yi Zheng, Yuanbo Gong, Jinshi Xu, Chuanfeng Li, and Guangcan Guo, " The spatial state of biphotons: physics and applications in quantum imaging", Advanced Imaging 3 4, B00003 (2026).

[37] Sakthi Priya Amirtharaj, Guruprasad Patil, Harshavardhan Hajeri, Sabahat Sakinah, Aryan Bhardwaj, Ashutosh Kumar Singh, Sanjay Sabu, Balakrishnan Viswanathan, Prem B Bisht, and Anil Prabhakar, "Optical Sources for Applications in Quantum Technologies", (2025).

[38] Emma Brambila, René Sondenheimer, Marta Gilaberte, Valerio Gili, and Markus Gräfe, Frontiers in Optics + Laser Science 2024 (FiO, LS) JW5A.51 (2024) ISBN:978-1-957171-95-1.

[39] Jorge Fuenzalida, Marta Gilaberte Basset, Sebastian Töpfer, Juan P. Torres, and Markus Gräfe, "Experimental quantum imaging distillation with undetected light", Science Advances 9 35, eadg9573 (2023).

[40] Bochen Wang, Yansheng Bao, Zhengyong Li, Changyong Tian, and Yong-Chun Liu, "Frequency-angular spectrum of entangled photon pairs generated by focused pump", Optik 289, 171283 (2023).

[41] Gabriela Barreto Lemos, Mayukh Lahiri, Sven Ramelow, Radek Lapkiewicz, and William N. Plick, "Quantum imaging and metrology with undetected photons: tutorial", Journal of the Optical Society of America B 39 8, 2200 (2022).

[42] Santiago Lopez-Huidobro, Mohammad Noureddin, Maria V. Chekhova, and Nicolas Y. Joly, "Tunable fiber source of entangled UV-C and infrared photons", Optics Letters 48 13, 3423 (2023).

[43] Satyajeet Patil, Rajshree Swarnkar, Jonas L. Moos, Sebastian Töpfer, Sergio Tovar‐Pérez, Jorge Fuenzalida, and Markus Gräfe, "Advances in Position‐Momentum Entanglement: A Versatile Tool for Quantum Technologies", Laser & Photonics Reviews 20 15, e01358 (2026).

[44] Paul Kinsler, Martin W McCall, Rupert F Oulton, and Alex S Clark, "The surprising persistence of time-dependent quantum entanglement", New Journal of Physics 24 10, 103037 (2022).

[45] Hashir Kuniyil, Asad Ali, and Saif Al-Kuwari, "Entanglement certification in bulk nonlinear crystals for degenerate and nondegenerate spontaneous parametric down conversion: Spectral filter effects on transverse spatial correlations", Physical Review A 113 5, 052607 (2026).

[46] Elkin A. Santos, Thomas Pertsch, Frank Setzpfandt, and Sina Saravi, "Subdiffraction Quantum Imaging with Undetected Photons", Physical Review Letters 128 17, 173601 (2022).

[47] Preetisha Goswami, Marta Gilaberte Basset, Jorge Fuenzalida, Markus Gräfe, and Valerio Flavio Gili, "Non-degenerate SPDC photon-pair source for UV-A illumination", Optics Express 33 22, 45779 (2025).

[48] Inna Kviatkovsky, Helen M. Chrzanowski, and Sven Ramelow, "Mid-infrared microscopy via position correlations of undetected photons", Optics Express 30 4, 5916 (2022).

[49] Balakrishnan Viswanathan, Gabriela Barreto Lemos, and Mayukh Lahiri, "Position correlation enabled quantum imaging with undetected photons", Optics Letters 46 15, 3496 (2021).

[50] Balakrishnan Viswanathan, Gabriela Barreto Lemos, and Mayukh Lahiri, "Resolution limit in quantum imaging with undetected photons using position correlations", Optics Express 29 23, 38185 (2021).

[51] Marta Gilaberte Basset, Armin Hochrainer, Sebastian Töpfer, Felix Riexinger, Patricia Bickert, Josué Ricardo León-Torres, Fabian Steinlechner, and Markus Gräfe, "Video-Rate Imaging with Undetected Photons", Laser & Photonics Reviews 15 6, 2000327 (2021).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-10 20:51:11) and SAO/NASA ADS (last updated successfully 2026-08-10 20:51:18). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.