[{"language":[{"iso":"eng"}],"publication":"Optica","abstract":[{"text":"<jats:p>\r\n                    Precise measurements of both the arrival time and carrier frequency of light pulses are essential for time–frequency-encoded quantum technologies. Quantum mechanics, however, imposes fundamental limits on the simultaneous determination of these quantities. In this work, we derive and experimentally verify the quantum uncertainty bounds governing joint time–frequency measurements. We show that when detection is restricted to finite time windows, the problem is naturally described by a quantum rotor, rendering the commonly used Heisenberg uncertainty relation inapplicable. We further propose an optimal detection scheme that saturates these fundamental limits. By sampling the\r\n                    <jats:italic toggle=\"yes\">Q</jats:italic>\r\n                    -function, we demonstrate the reconstruction of the Wigner function beyond the harmonic oscillator. Using an experimental implementation based on a quantum pulse gate, we confirm that the proposed scheme approaches the ultimate quantum limit for simultaneous time–frequency measurements. These results provide a framework for joint time–frequency detection with direct implications for precision measurements and quantum information processing.\r\n                  </jats:p>","lang":"eng"}],"publisher":"Optica Publishing Group","date_created":"2026-03-23T12:30:02Z","title":"Quantum-limited detection of the arrival time and the carrier frequency of time-dependent signals","issue":"3","year":"2026","_id":"65096","department":[{"_id":"15"},{"_id":"623"},{"_id":"288"}],"user_id":"27150","article_number":"548","type":"journal_article","status":"public","date_updated":"2026-03-25T07:59:23Z","volume":13,"author":[{"id":"88605","full_name":"Folge, Patrick Fabian","last_name":"Folge","first_name":"Patrick Fabian"},{"first_name":"Laura Maria","full_name":"Serino, Laura Maria","id":"88242","last_name":"Serino"},{"first_name":"Ladislav","last_name":"Mišta","full_name":"Mišta, Ladislav"},{"first_name":"Benjamin","last_name":"Brecht","orcid":"0000-0003-4140-0556 ","full_name":"Brecht, Benjamin","id":"27150"},{"last_name":"Silberhorn","full_name":"Silberhorn, Christine","id":"26263","first_name":"Christine"},{"first_name":"Jaroslav","full_name":"Řeháček, Jaroslav","last_name":"Řeháček"},{"last_name":"Hradil","full_name":"Hradil, Zdeněk","first_name":"Zdeněk"}],"doi":"10.1364/optica.579459","publication_identifier":{"issn":["2334-2536"]},"publication_status":"published","intvolume":"        13","citation":{"short":"P.F. Folge, L.M. Serino, L. Mišta, B. Brecht, C. Silberhorn, J. Řeháček, Z. Hradil, Optica 13 (2026).","bibtex":"@article{Folge_Serino_Mišta_Brecht_Silberhorn_Řeháček_Hradil_2026, title={Quantum-limited detection of the arrival time and the carrier frequency of time-dependent signals}, volume={13}, DOI={<a href=\"https://doi.org/10.1364/optica.579459\">10.1364/optica.579459</a>}, number={3548}, journal={Optica}, publisher={Optica Publishing Group}, author={Folge, Patrick Fabian and Serino, Laura Maria and Mišta, Ladislav and Brecht, Benjamin and Silberhorn, Christine and Řeháček, Jaroslav and Hradil, Zdeněk}, year={2026} }","mla":"Folge, Patrick Fabian, et al. “Quantum-Limited Detection of the Arrival Time and the Carrier Frequency of Time-Dependent Signals.” <i>Optica</i>, vol. 13, no. 3, 548, Optica Publishing Group, 2026, doi:<a href=\"https://doi.org/10.1364/optica.579459\">10.1364/optica.579459</a>.","apa":"Folge, P. F., Serino, L. M., Mišta, L., Brecht, B., Silberhorn, C., Řeháček, J., &#38; Hradil, Z. (2026). Quantum-limited detection of the arrival time and the carrier frequency of time-dependent signals. <i>Optica</i>, <i>13</i>(3), Article 548. <a href=\"https://doi.org/10.1364/optica.579459\">https://doi.org/10.1364/optica.579459</a>","ama":"Folge PF, Serino LM, Mišta L, et al. Quantum-limited detection of the arrival time and the carrier frequency of time-dependent signals. <i>Optica</i>. 2026;13(3). doi:<a href=\"https://doi.org/10.1364/optica.579459\">10.1364/optica.579459</a>","chicago":"Folge, Patrick Fabian, Laura Maria Serino, Ladislav Mišta, Benjamin Brecht, Christine Silberhorn, Jaroslav Řeháček, and Zdeněk Hradil. “Quantum-Limited Detection of the Arrival Time and the Carrier Frequency of Time-Dependent Signals.” <i>Optica</i> 13, no. 3 (2026). <a href=\"https://doi.org/10.1364/optica.579459\">https://doi.org/10.1364/optica.579459</a>.","ieee":"P. F. Folge <i>et al.</i>, “Quantum-limited detection of the arrival time and the carrier frequency of time-dependent signals,” <i>Optica</i>, vol. 13, no. 3, Art. no. 548, 2026, doi: <a href=\"https://doi.org/10.1364/optica.579459\">10.1364/optica.579459</a>."}},{"abstract":[{"lang":"eng","text":"<jats:p>The characterization of the complex spectral amplitude, that is, the spectrum and spectral phase, of single-photon-level light fields is a crucial capability for modern photonic quantum technologies. Since established pulse characterization techniques are not applicable at low intensities, alternative approaches are required. Here, we demonstrate the retrieval of the complex spectral amplitude of single-photon-level light pulses through measuring their chronocyclic <jats:italic toggle=\"yes\">Q</jats:italic> −function. Our approach draws inspiration from quantum state tomography by exploiting the analogy between quadrature phase space and time-frequency phase space. In the experiment, we perform time-frequency projections with a quantum pulse gate (QPG), which directly yield the chronocyclic <jats:italic toggle=\"yes\">Q</jats:italic> −function. We evaluate the complex spectral amplitude from the measured chronocyclic <jats:italic toggle=\"yes\">Q</jats:italic> −function data with maximum likelihood estimation (MLE), which is the established technique for quantum state tomography. The MLE yields not only an unambigious estimate of the complex spectral amplitude of the state under test that does not require any <jats:italic toggle=\"yes\">a priori</jats:italic> information, but also allows for, in principle, estimating the spectral-temporal coherence properties of the state. Our method accurately recovers features such as jumps in the spectral phase and is resistant against regions with zero spectral intensity, which makes it immediately beneficial for classical pulse characterization problems.</jats:p>"}],"status":"public","type":"journal_article","publication":"Optics Express","article_number":"5551","language":[{"iso":"eng"}],"_id":"63216","user_id":"27150","department":[{"_id":"15"},{"_id":"623"}],"year":"2024","citation":{"ieee":"A. Bhattacharjee <i>et al.</i>, “Pulse characterization at the single-photon level through chronocyclic <i>Q</i>-function measurements,” <i>Optics Express</i>, vol. 33, no. 3, Art. no. 5551, 2024, doi: <a href=\"https://doi.org/10.1364/oe.540125\">10.1364/oe.540125</a>.","chicago":"Bhattacharjee, Abhinandan, Patrick Fabian Folge, Laura Maria Serino, Jaroslav Řeháček, Zdeněk Hradil, Christine Silberhorn, and Benjamin Brecht. “Pulse Characterization at the Single-Photon Level through Chronocyclic <i>Q</i>-Function Measurements.” <i>Optics Express</i> 33, no. 3 (2024). <a href=\"https://doi.org/10.1364/oe.540125\">https://doi.org/10.1364/oe.540125</a>.","ama":"Bhattacharjee A, Folge PF, Serino LM, et al. Pulse characterization at the single-photon level through chronocyclic <i>Q</i>-function measurements. <i>Optics Express</i>. 2024;33(3). doi:<a href=\"https://doi.org/10.1364/oe.540125\">10.1364/oe.540125</a>","short":"A. Bhattacharjee, P.F. Folge, L.M. Serino, J. Řeháček, Z. Hradil, C. Silberhorn, B. Brecht, Optics Express 33 (2024).","bibtex":"@article{Bhattacharjee_Folge_Serino_Řeháček_Hradil_Silberhorn_Brecht_2024, title={Pulse characterization at the single-photon level through chronocyclic <i>Q</i>-function measurements}, volume={33}, DOI={<a href=\"https://doi.org/10.1364/oe.540125\">10.1364/oe.540125</a>}, number={35551}, journal={Optics Express}, publisher={Optica Publishing Group}, author={Bhattacharjee, Abhinandan and Folge, Patrick Fabian and Serino, Laura Maria and Řeháček, Jaroslav and Hradil, Zdeněk and Silberhorn, Christine and Brecht, Benjamin}, year={2024} }","mla":"Bhattacharjee, Abhinandan, et al. “Pulse Characterization at the Single-Photon Level through Chronocyclic <i>Q</i>-Function Measurements.” <i>Optics Express</i>, vol. 33, no. 3, 5551, Optica Publishing Group, 2024, doi:<a href=\"https://doi.org/10.1364/oe.540125\">10.1364/oe.540125</a>.","apa":"Bhattacharjee, A., Folge, P. F., Serino, L. M., Řeháček, J., Hradil, Z., Silberhorn, C., &#38; Brecht, B. (2024). Pulse characterization at the single-photon level through chronocyclic <i>Q</i>-function measurements. <i>Optics Express</i>, <i>33</i>(3), Article 5551. <a href=\"https://doi.org/10.1364/oe.540125\">https://doi.org/10.1364/oe.540125</a>"},"intvolume":"        33","publication_status":"published","publication_identifier":{"issn":["1094-4087"]},"issue":"3","title":"Pulse characterization at the single-photon level through chronocyclic <i>Q</i>-function measurements","doi":"10.1364/oe.540125","date_updated":"2025-12-18T16:08:40Z","publisher":"Optica Publishing Group","author":[{"full_name":"Bhattacharjee, Abhinandan","id":"95902","last_name":"Bhattacharjee","first_name":"Abhinandan"},{"first_name":"Patrick Fabian","last_name":"Folge","full_name":"Folge, Patrick Fabian","id":"88605"},{"first_name":"Laura Maria","last_name":"Serino","id":"88242","full_name":"Serino, Laura Maria"},{"first_name":"Jaroslav","last_name":"Řeháček","full_name":"Řeháček, Jaroslav"},{"first_name":"Zdeněk","full_name":"Hradil, Zdeněk","last_name":"Hradil"},{"full_name":"Silberhorn, Christine","id":"26263","last_name":"Silberhorn","first_name":"Christine"},{"first_name":"Benjamin","last_name":"Brecht","orcid":"0000-0003-4140-0556 ","id":"27150","full_name":"Brecht, Benjamin"}],"date_created":"2025-12-18T16:08:16Z","volume":33},{"issue":"4","publication_identifier":{"issn":["2691-3399"]},"publication_status":"published","intvolume":"         5","citation":{"mla":"Folge, Patrick Fabian, et al. “A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates.” <i>PRX Quantum</i>, vol. 5, no. 4, 040329, American Physical Society (APS), 2024, doi:<a href=\"https://doi.org/10.1103/prxquantum.5.040329\">10.1103/prxquantum.5.040329</a>.","short":"P.F. Folge, M. Stefszky, B. Brecht, C. Silberhorn, PRX Quantum 5 (2024).","bibtex":"@article{Folge_Stefszky_Brecht_Silberhorn_2024, title={A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates}, volume={5}, DOI={<a href=\"https://doi.org/10.1103/prxquantum.5.040329\">10.1103/prxquantum.5.040329</a>}, number={4040329}, journal={PRX Quantum}, publisher={American Physical Society (APS)}, author={Folge, Patrick Fabian and Stefszky, Michael and Brecht, Benjamin and Silberhorn, Christine}, year={2024} }","apa":"Folge, P. F., Stefszky, M., Brecht, B., &#38; Silberhorn, C. (2024). A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates. <i>PRX Quantum</i>, <i>5</i>(4), Article 040329. <a href=\"https://doi.org/10.1103/prxquantum.5.040329\">https://doi.org/10.1103/prxquantum.5.040329</a>","ieee":"P. F. Folge, M. Stefszky, B. Brecht, and C. Silberhorn, “A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates,” <i>PRX Quantum</i>, vol. 5, no. 4, Art. no. 040329, 2024, doi: <a href=\"https://doi.org/10.1103/prxquantum.5.040329\">10.1103/prxquantum.5.040329</a>.","chicago":"Folge, Patrick Fabian, Michael Stefszky, Benjamin Brecht, and Christine Silberhorn. “A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates.” <i>PRX Quantum</i> 5, no. 4 (2024). <a href=\"https://doi.org/10.1103/prxquantum.5.040329\">https://doi.org/10.1103/prxquantum.5.040329</a>.","ama":"Folge PF, Stefszky M, Brecht B, Silberhorn C. A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates. <i>PRX Quantum</i>. 2024;5(4). doi:<a href=\"https://doi.org/10.1103/prxquantum.5.040329\">10.1103/prxquantum.5.040329</a>"},"year":"2024","volume":5,"author":[{"first_name":"Patrick Fabian","last_name":"Folge","id":"88605","full_name":"Folge, Patrick Fabian"},{"first_name":"Michael","last_name":"Stefszky","id":"42777","full_name":"Stefszky, Michael"},{"first_name":"Benjamin","id":"27150","full_name":"Brecht, Benjamin","orcid":"0000-0003-4140-0556 ","last_name":"Brecht"},{"id":"26263","full_name":"Silberhorn, Christine","last_name":"Silberhorn","first_name":"Christine"}],"date_created":"2025-12-18T16:10:37Z","date_updated":"2025-12-18T16:10:55Z","publisher":"American Physical Society (APS)","doi":"10.1103/prxquantum.5.040329","title":"A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates","publication":"PRX Quantum","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"<jats:p>Linear optical quantum networks, consisting of a quantum input state and a multiport interferometer, are an important building block for many quantum technological concepts, e.g., Gaussian boson sampling. Here, we propose the implementation of such networks based on frequency conversion by utilizing a so-called multioutput quantum pulse gate (MQPG). This approach allows the resource-efficient and therefore scalable implementation of frequency-bin-based, fully programmable interferometers in a single spatial and polarization mode. Quantum input states for this network can be provided by utilizing the strong frequency entanglement of a type-0 parametric down-conversion (PDC) source. Here, we develop a theoretical framework to describe linear networks based on an MQPG and PDC and utilize it to investigate the limits and scalabilty of our approach.</jats:p>\r\n          <jats:sec>\r\n            <jats:title/>\r\n            <jats:supplementary-material>\r\n              <jats:permissions>\r\n                <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement>\r\n                <jats:copyright-year>2024</jats:copyright-year>\r\n              </jats:permissions>\r\n            </jats:supplementary-material>\r\n          </jats:sec>"}],"department":[{"_id":"15"},{"_id":"623"}],"user_id":"27150","_id":"63218","language":[{"iso":"eng"}],"article_number":"040329"},{"title":"A Pulsed Lidar System With Ultimate Quantum Range Accuracy","doi":"10.1109/lpt.2023.3277515","date_updated":"2023-06-06T10:13:05Z","publisher":"Institute of Electrical and Electronics Engineers (IEEE)","author":[{"full_name":"Kruse, Stephan","id":"38254","last_name":"Kruse","first_name":"Stephan"},{"first_name":"Laura","id":"88242","full_name":"Serino, Laura","last_name":"Serino"},{"first_name":"Patrick Fabian","last_name":"Folge","id":"88605","full_name":"Folge, Patrick Fabian"},{"first_name":"Dana","full_name":"Echeverria Oviedo, Dana","last_name":"Echeverria Oviedo"},{"last_name":"Bhattacharjee","full_name":"Bhattacharjee, Abhinandan","first_name":"Abhinandan"},{"first_name":"Michael","last_name":"Stefszky","full_name":"Stefszky, Michael","id":"42777"},{"orcid":"0000-0002-5950-6618 ","last_name":"Scheytt","full_name":"Scheytt, J. Christoph","id":"37144","first_name":"J. Christoph"},{"orcid":"0000-0003-4140-0556 ","last_name":"Brecht","id":"27150","full_name":"Brecht, Benjamin","first_name":"Benjamin"},{"first_name":"Christine","last_name":"Silberhorn","full_name":"Silberhorn, Christine","id":"26263"}],"date_created":"2023-06-06T10:09:05Z","volume":35,"year":"2023","citation":{"apa":"Kruse, S., Serino, L., Folge, P. F., Echeverria Oviedo, D., Bhattacharjee, A., Stefszky, M., Scheytt, J. C., Brecht, B., &#38; Silberhorn, C. (2023). A Pulsed Lidar System With Ultimate Quantum Range Accuracy. <i>IEEE Photonics Technology Letters</i>, <i>35</i>(14), 769–772. <a href=\"https://doi.org/10.1109/lpt.2023.3277515\">https://doi.org/10.1109/lpt.2023.3277515</a>","bibtex":"@article{Kruse_Serino_Folge_Echeverria Oviedo_Bhattacharjee_Stefszky_Scheytt_Brecht_Silberhorn_2023, title={A Pulsed Lidar System With Ultimate Quantum Range Accuracy}, volume={35}, DOI={<a href=\"https://doi.org/10.1109/lpt.2023.3277515\">10.1109/lpt.2023.3277515</a>}, number={14}, journal={IEEE Photonics Technology Letters}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Kruse, Stephan and Serino, Laura and Folge, Patrick Fabian and Echeverria Oviedo, Dana and Bhattacharjee, Abhinandan and Stefszky, Michael and Scheytt, J. Christoph and Brecht, Benjamin and Silberhorn, Christine}, year={2023}, pages={769–772} }","short":"S. Kruse, L. Serino, P.F. Folge, D. Echeverria Oviedo, A. Bhattacharjee, M. Stefszky, J.C. Scheytt, B. Brecht, C. Silberhorn, IEEE Photonics Technology Letters 35 (2023) 769–772.","mla":"Kruse, Stephan, et al. “A Pulsed Lidar System With Ultimate Quantum Range Accuracy.” <i>IEEE Photonics Technology Letters</i>, vol. 35, no. 14, Institute of Electrical and Electronics Engineers (IEEE), 2023, pp. 769–72, doi:<a href=\"https://doi.org/10.1109/lpt.2023.3277515\">10.1109/lpt.2023.3277515</a>.","ieee":"S. Kruse <i>et al.</i>, “A Pulsed Lidar System With Ultimate Quantum Range Accuracy,” <i>IEEE Photonics Technology Letters</i>, vol. 35, no. 14, pp. 769–772, 2023, doi: <a href=\"https://doi.org/10.1109/lpt.2023.3277515\">10.1109/lpt.2023.3277515</a>.","chicago":"Kruse, Stephan, Laura Serino, Patrick Fabian Folge, Dana Echeverria Oviedo, Abhinandan Bhattacharjee, Michael Stefszky, J. Christoph Scheytt, Benjamin Brecht, and Christine Silberhorn. “A Pulsed Lidar System With Ultimate Quantum Range Accuracy.” <i>IEEE Photonics Technology Letters</i> 35, no. 14 (2023): 769–72. <a href=\"https://doi.org/10.1109/lpt.2023.3277515\">https://doi.org/10.1109/lpt.2023.3277515</a>.","ama":"Kruse S, Serino L, Folge PF, et al. A Pulsed Lidar System With Ultimate Quantum Range Accuracy. <i>IEEE Photonics Technology Letters</i>. 2023;35(14):769-772. doi:<a href=\"https://doi.org/10.1109/lpt.2023.3277515\">10.1109/lpt.2023.3277515</a>"},"intvolume":"        35","page":"769-772","publication_status":"published","publication_identifier":{"issn":["1041-1135","1941-0174"]},"issue":"14","keyword":["Electrical and Electronic Engineering","Atomic and Molecular Physics","and Optics","Electronic","Optical and Magnetic Materials"],"language":[{"iso":"eng"}],"_id":"45485","user_id":"27150","department":[{"_id":"15"},{"_id":"58"},{"_id":"623"},{"_id":"230"},{"_id":"288"}],"status":"public","type":"journal_article","publication":"IEEE Photonics Technology Letters"}]