{"id":154818,"date":"2023-01-07T16:22:26","date_gmt":"2023-01-07T22:22:26","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2023\/01\/interaction-free-single-pixel-quantum-imaging-with-undetected-photons"},"modified":"2023-01-07T16:22:26","modified_gmt":"2023-01-07T22:22:26","slug":"interaction-free-single-pixel-quantum-imaging-with-undetected-photons","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2023\/01\/interaction-free-single-pixel-quantum-imaging-with-undetected-photons","title":{"rendered":"Interaction-free, single-pixel quantum imaging with undetected photons"},"content":{"rendered":"<p style=\"padding-right: 20px\"><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/interaction-free-single-pixel-quantum-imaging-with-undetected-photons.jpg\"><\/a><\/p>\n<p>Over the past few decades, several imaging protocols based on quantum technologies have been realized<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 1\" title=\"Genovese, M. Real application of quantum imaging. J. Opt. 18, 073002 (2016).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR1\" id=\"ref-link-section-d143387938e442\">1<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 2\" title=\"Moreau, P., Toninelli, E., Gregory, T. & Padgett, M. J. Imaging with quantum states of light. Nat. Rev. Phys. 1367&ndash;380 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR2\" id=\"ref-link-section-d143387938e445\">2<\/a><\/sup>, which have expanded the application capabilities of optical imaging. These include ghost imaging (GI)<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 3\" title=\"Pittman, T., Shih, Y. H., Strekalov, D. V. & Sergienko, A. V. Optical imaging by means of two-photon quantum entanglement. Phys. Rev. A 52, R3429&ndash;R3432 (1995).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR3\" id=\"ref-link-section-d143387938e449\">3<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 4\" title=\"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&ndash;3603 (1995).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR4\" id=\"ref-link-section-d143387938e452\">4<\/a><\/sup>, quantum imaging with undetected photons (QIUP)<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 5\" title=\"Lemos, G. B. et al. Quantum imaging with undetected photons. Nature 512409&ndash;412 (2014).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR5\" id=\"ref-link-section-d143387938e456\">5<\/a><\/sup>, and interaction-free measurements (IFMs)<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 6\" title=\"Dicke, R. H. Interaction-free quantum measurements: A paradox? Am. J. Phys. 49,925 (1981).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR6\" id=\"ref-link-section-d143387938e460\">6<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 7\" title=\"Elitzur, A. C. & Vaidman, L. Quantum mechanical interaction-free measurements. Found. Phys. 23987&ndash;997 (1993).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR7\" id=\"ref-link-section-d143387938e463\">7<\/a><\/sup>. The quantum GI scheme relies on the spatial correlations of entangled photon pairs and requires two-photon coincident measurements. Furthermore, ghost imaging can also be realized with classical intensity-fluctuation correlations<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 8\" title=\"Shapiro, J. H. & Boyd, R. W. The physics of ghost imaging. Quantum Inf. Process 11949&ndash;993 (2012).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR8\" id=\"ref-link-section-d143387938e467\">8<\/a><\/sup>. Later, various single-pixel imaging (SPI) protocols were proposed<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Shapiro, J. H. Computational ghost imaging. Phys. Rev. A. 78, 061802 (2008). (R).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR9\" id=\"ref-link-section-d143387938e472\">9<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Duarte, M. F. et al. Single-pixel imaging via compressive sampling. IEEE Signal Process. Mag. 25, 83&ndash;91 (2008).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR10\" id=\"ref-link-section-d143387938e472_1\">10<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Altmann, Y. et al. Quantum-inspired computational imaging. Science 361,660 (2018).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR11\" id=\"ref-link-section-d143387938e472_2\">11<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Edgar, M. P., Gibson, G. M. & Padgett, M. J. Principles and prospects for single-pixel imaging. Nat. Photonics 13, 13&ndash;20 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR12\" id=\"ref-link-section-d143387938e472_3\">12<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 13\" title=\"Gibson, G. M., Johnson, S. D. & Padgett, M. J. Single-pixel imaging 12 years on: a review. Opt. Exp. 28, 28190&ndash;28208 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR13\" id=\"ref-link-section-d143387938e475\">13<\/a><\/sup>, where the spatial correlations are not between two photons but between one photon and a programmable mask held in a spatial light modulator (SLM).<\/p>\n<p>In contrast to modern digital cameras employing array sensors to capture images, SPI use a sequence of masks to interrogate the scene along with the correlated intensity measurements by a single-pixel detector. The spatially resolved masks are usually generated by computer and displayed by SLM. Combined with compressive techniques<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 10\" title=\"Duarte, M. F. et al. Single-pixel imaging via compressive sampling. IEEE Signal Process. Mag. 25, 83&ndash;91 (2008).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR10\" id=\"ref-link-section-d143387938e482\">10<\/a><\/sup>, the number of sampling measurements is fewer than the total number of pixels in the image. Thereby, SPI can reduce the data processing requirement, and shows potential capability for high dimensional sensing<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 12\" title=\"Edgar, M. P., Gibson, G. M. & Padgett, M. J. Principles and prospects for single-pixel imaging. Nat. Photonics 13, 13&ndash;20 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR12\" id=\"ref-link-section-d143387938e486\">12<\/a><\/sup>. On the other hand, the modern single-photon detector is featured by improved detection efficiency, lower dark counts, and faster timing response<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 14\" title=\"Hadfield, R. H. Single-photon detectors for optical quantum information applications. Nat. Photonics 3696&ndash;705 (2009).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR14\" id=\"ref-link-section-d143387938e490\">14<\/a><\/sup>. Such enhancements have significance to applying SPI into weak signal detection scenarios, such as scattering medium imaging or long-range 3D imaging<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 11\" title=\"Altmann, Y. et al. Quantum-inspired computational imaging. Science 361,660 (2018).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR11\" id=\"ref-link-section-d143387938e494\">11<\/a><\/sup>.<\/p>\n<p>The QIUP scheme is based on induced coherence (IC), which was first proposed by Zou, Wang, and Mandel<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 15\" title=\"Zou, X. Y., Wang, L. J. & Mandel, L. Induced coherence and indistinguishability in optical interference. Phys. Rev. Lett. 67318&ndash;321 (1991).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR15\" id=\"ref-link-section-d143387938e501\">15<\/a><\/sup>. They used two photon sources to generate photon pairs. By overlapping path of two sources for one photon (idler)<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Zou, X. Y., Wang, L. J. & Mandel, L. Induced coherence and indistinguishability in optical interference. Phys. Rev. Lett. 67318&ndash;321 (1991).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR15\" id=\"ref-link-section-d143387938e505\">15<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Wang, L. J., Zou, X. Y. & Mandel, L. Induced coherence without induced emission. Phys. Rev. A. 44, 4614&ndash;4622 (1991).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR16\" id=\"ref-link-section-d143387938e505_1\">16<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 17\" title=\"Herzog, T. J., Rarity, J. G., Weinfurter, H. & Zeilinger, A. Frustrated two-photon creation via Interference. Phys. Rev. Lett. 72629&ndash;632 (1994).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR17\" id=\"ref-link-section-d143387938e508\">17<\/a><\/sup> and establishing the so-called path identity<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 18\" title=\"Krenn, M., Hochrainer, A., Lahiri, M. & Zeilinger, A. Entanglement by path identity. Phys. Rev. Lett. 118, 080401 (2017).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR18\" id=\"ref-link-section-d143387938e512\">18<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 19\" title=\"Hochrainer, A., Lahiri, M., Erhard, M., Krenn, M. & Zeilinger, A. Quantum indistinguishability by path identity and with undetected photons,. Rev. Mod. Phys. 94, 025007 (2022).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR19\" id=\"ref-link-section-d143387938e515\">19<\/a><\/sup>, there is no information about the origin of the other photon (signal). Thus, the signal photon is in the superposition state of being created in either of the sources. The phase and transmissivity of the idler photon are encoded in the interference of the signal photon. Inserting one object onto the idler path between two sources, one can obtain images exclusively with the signal photons which have no interaction with the object<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 5\" title=\"Lemos, G. B. et al. Quantum imaging with undetected photons. Nature 512409&ndash;412 (2014).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR5\" id=\"ref-link-section-d143387938e519\">5<\/a><\/sup>. In contrast to GI, QIUP does not involve the detection of the photon illuminating the object or any coincidence measurement. This is an advantage of QIUP, as the wavelength of the detected photon can be chosen independently from that of the photon interacting with the object<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 5\" title=\"Lemos, G. B. et al. Quantum imaging with undetected photons. Nature 512409&ndash;412 (2014).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR5\" id=\"ref-link-section-d143387938e523\">5<\/a><\/sup>. This concept was further explored in infrared (IR) spectroscopy<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 20\" title=\"Kalashnikov, D. A., Paterova, A. V., Kulik, S. P. & Krivitsky, L. A. Infrared spectroscopy with visible light. Nat. Photonics 10, 98&ndash;101 (2016).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR20\" id=\"ref-link-section-d143387938e528\">20<\/a><\/sup>, optical coherence tomography<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 21\" title=\"Vall\u00e9s, A., Jim\u00e9nez, G., Salazar-Serrano, L. J. & Torres, J. P. Optical sectioning in induced coherence tomography with frequency-entangled photons. Phys. Rev. A. 97, 023824 (2018).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR21\" id=\"ref-link-section-d143387938e532\">21<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 22\" title=\"Paterova, A. V., Yang, H., An, C., Kalashnikov, D. A. & Krivitsky, L. A. Tunable optical coherence tomography in the infrared range using visible photons. Quantum Sci. Technol. 3, 025008 (2018).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR22\" id=\"ref-link-section-d143387938e535\">22<\/a><\/sup>, mid-IR imaging<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Kviatkovsky, I., Chrzanowski, H. M., Avery, E. G., Bartolomaeus, H. & Ramelow, S. Microscopy with undetected photons in the mid-infrared. Sci. Adv. 6, eabd0264 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR23\" id=\"ref-link-section-d143387938e539\">23<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Paterova, A. V., Maniam, S. M., Yang, H., Grenci, G. & Krivitsky, L. A. Hyperspectral infrared microscopy with visible light. Sci. Adv. 6, eabd0460 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR24\" id=\"ref-link-section-d143387938e539_1\">24<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 25\" title=\"Paterova, A. V., Yang, H., Toa, Z. S. D. & Krivitsky, L. A. Quantum imaging for the semiconductor industry. Appl. Phys. Lett. 117, 054004 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR25\" id=\"ref-link-section-d143387938e542\">25<\/a><\/sup>, terahertz (THz) sensing<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 26\" title=\"Kutas, M. et al. Terahertz quantum sensing. Sci. Adv. 6, eaaz8065 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR26\" id=\"ref-link-section-d143387938e546\">26<\/a><\/sup>, biological microscopy<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 27\" title=\"B\u00faz\u00e0s, A., Wolff, E. K., Benedict, M. G., Ormos, P. & D\u00e9r, A. Biological microscopy with undetected photons. IEEE Access 8, 107539&ndash;107548 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR27\" id=\"ref-link-section-d143387938e550\">27<\/a><\/sup>, and holography<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 28\" title=\"T\u00f6pfer, S. et al. Quantum holography with undetected light. Sci. Adv. 8, eabl4301 (2022).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR28\" id=\"ref-link-section-d143387938e554\">28<\/a><\/sup>. Recently, the related SU(1,1) interferometer has been investigated and employed in quantum-enhanced metrology<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Yurke, B., McCall, S. L. & Klauder, J. R. SU and SU(1,1) interferometers. Phys. Rev. A. 33, 4033&ndash;4054 (1986).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR29\" id=\"ref-link-section-d143387938e559\">29<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Hudelist, F. et al. Quantum metrology with parametric amplifier-based photon correlation interferometers. Nat. Commun. 5, 3049 (2014).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR30\" id=\"ref-link-section-d143387938e559_1\">30<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Chekhova, M. V. & Ou, Z. Y. Nonlinear interferometers in quantum optics. Adv. Opt. Photonics 8104&ndash;155 (2016).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR31\" id=\"ref-link-section-d143387938e559_2\">31<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Ou, Z. Y. & Li, X. Quantum SU(1,1) interferometers: basic principles and applications. APL Photonics 5, 080902 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR32\" id=\"ref-link-section-d143387938e559_3\">32<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 33\" title=\"Du, W. et al. SU-in-SU(1,1) Nested interferometer for high sensitivity, loss-tolerant quantum metrology. Phys. Rev. Lett. 128, 033601 (2022).\" href=\"https:\/\/www.nature.com\/articles\/s41534-022-00673-6#ref-CR33\" id=\"ref-link-section-d143387938e562\">33<\/a><\/sup>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Over the past few decades, several imaging protocols based on quantum technologies have been realized1,2, which have expanded the application capabilities of optical imaging. These include ghost imaging (GI)3,4, quantum imaging with undetected photons (QIUP)5, and interaction-free measurements (IFMs)6,7. The quantum GI scheme relies on the spatial correlations of entangled photon pairs and requires two-photon [\u2026]<\/p>\n","protected":false},"author":534,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,1523,1617],"tags":[],"class_list":["post-154818","post","type-post","status-publish","format-standard","hentry","category-biological","category-computing","category-quantum-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/154818","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/534"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=154818"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/154818\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=154818"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=154818"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=154818"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}