---
_id: '65096'
abstract:
- lang: eng
  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>"
article_number: '548'
author:
- first_name: Patrick Fabian
  full_name: Folge, Patrick Fabian
  id: '88605'
  last_name: Folge
- first_name: Laura Maria
  full_name: Serino, Laura Maria
  id: '88242'
  last_name: Serino
- first_name: Ladislav
  full_name: Mišta, Ladislav
  last_name: Mišta
- first_name: Benjamin
  full_name: Brecht, Benjamin
  id: '27150'
  last_name: Brecht
  orcid: '0000-0003-4140-0556 '
- first_name: Christine
  full_name: Silberhorn, Christine
  id: '26263'
  last_name: Silberhorn
- first_name: Jaroslav
  full_name: Řeháček, Jaroslav
  last_name: Řeháček
- first_name: Zdeněk
  full_name: Hradil, Zdeněk
  last_name: Hradil
citation:
  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>
  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>
  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}
    }'
  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>.'
  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>.
  short: P.F. Folge, L.M. Serino, L. Mišta, B. Brecht, C. Silberhorn, J. Řeháček,
    Z. Hradil, Optica 13 (2026).
date_created: 2026-03-23T12:30:02Z
date_updated: 2026-03-25T07:59:23Z
department:
- _id: '15'
- _id: '623'
- _id: '288'
doi: 10.1364/optica.579459
intvolume: '        13'
issue: '3'
language:
- iso: eng
publication: Optica
publication_identifier:
  issn:
  - 2334-2536
publication_status: published
publisher: Optica Publishing Group
status: public
title: Quantum-limited detection of the arrival time and the carrier frequency of
  time-dependent signals
type: journal_article
user_id: '27150'
volume: 13
year: '2026'
...
---
_id: '63216'
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>
article_number: '5551'
author:
- first_name: Abhinandan
  full_name: Bhattacharjee, Abhinandan
  id: '95902'
  last_name: Bhattacharjee
- first_name: Patrick Fabian
  full_name: Folge, Patrick Fabian
  id: '88605'
  last_name: Folge
- first_name: Laura Maria
  full_name: Serino, Laura Maria
  id: '88242'
  last_name: Serino
- first_name: Jaroslav
  full_name: Řeháček, Jaroslav
  last_name: Řeháček
- first_name: Zdeněk
  full_name: Hradil, Zdeněk
  last_name: Hradil
- first_name: Christine
  full_name: Silberhorn, Christine
  id: '26263'
  last_name: Silberhorn
- first_name: Benjamin
  full_name: Brecht, Benjamin
  id: '27150'
  last_name: Brecht
  orcid: '0000-0003-4140-0556 '
citation:
  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>
  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>
  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} }'
  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>.
  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>.'
  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>.
  short: A. Bhattacharjee, P.F. Folge, L.M. Serino, J. Řeháček, Z. Hradil, C. Silberhorn,
    B. Brecht, Optics Express 33 (2024).
date_created: 2025-12-18T16:08:16Z
date_updated: 2025-12-18T16:08:40Z
department:
- _id: '15'
- _id: '623'
doi: 10.1364/oe.540125
intvolume: '        33'
issue: '3'
language:
- iso: eng
publication: Optics Express
publication_identifier:
  issn:
  - 1094-4087
publication_status: published
publisher: Optica Publishing Group
status: public
title: Pulse characterization at the single-photon level through chronocyclic <i>Q</i>-function
  measurements
type: journal_article
user_id: '27150'
volume: 33
year: '2024'
...
---
_id: '63218'
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>"
article_number: '040329'
author:
- first_name: Patrick Fabian
  full_name: Folge, Patrick Fabian
  id: '88605'
  last_name: Folge
- first_name: Michael
  full_name: Stefszky, Michael
  id: '42777'
  last_name: Stefszky
- first_name: Benjamin
  full_name: Brecht, Benjamin
  id: '27150'
  last_name: Brecht
  orcid: '0000-0003-4140-0556 '
- first_name: Christine
  full_name: Silberhorn, Christine
  id: '26263'
  last_name: Silberhorn
citation:
  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>
  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>
  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} }'
  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>.
  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>.'
  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).
date_created: 2025-12-18T16:10:37Z
date_updated: 2025-12-18T16:10:55Z
department:
- _id: '15'
- _id: '623'
doi: 10.1103/prxquantum.5.040329
intvolume: '         5'
issue: '4'
language:
- iso: eng
publication: PRX Quantum
publication_identifier:
  issn:
  - 2691-3399
publication_status: published
publisher: American Physical Society (APS)
status: public
title: A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing
  Multioutput Quantum Pulse Gates
type: journal_article
user_id: '27150'
volume: 5
year: '2024'
...
---
_id: '45485'
author:
- first_name: Stephan
  full_name: Kruse, Stephan
  id: '38254'
  last_name: Kruse
- first_name: Laura
  full_name: Serino, Laura
  id: '88242'
  last_name: Serino
- first_name: Patrick Fabian
  full_name: Folge, Patrick Fabian
  id: '88605'
  last_name: Folge
- first_name: Dana
  full_name: Echeverria Oviedo, Dana
  last_name: Echeverria Oviedo
- first_name: Abhinandan
  full_name: Bhattacharjee, Abhinandan
  last_name: Bhattacharjee
- first_name: Michael
  full_name: Stefszky, Michael
  id: '42777'
  last_name: Stefszky
- first_name: J. Christoph
  full_name: Scheytt, J. Christoph
  id: '37144'
  last_name: Scheytt
  orcid: '0000-0002-5950-6618 '
- first_name: Benjamin
  full_name: Brecht, Benjamin
  id: '27150'
  last_name: Brecht
  orcid: '0000-0003-4140-0556 '
- first_name: Christine
  full_name: Silberhorn, Christine
  id: '26263'
  last_name: Silberhorn
citation:
  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>
  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} }'
  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>.'
  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>.'
  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>.
  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.
date_created: 2023-06-06T10:09:05Z
date_updated: 2023-06-06T10:13:05Z
department:
- _id: '15'
- _id: '58'
- _id: '623'
- _id: '230'
- _id: '288'
doi: 10.1109/lpt.2023.3277515
intvolume: '        35'
issue: '14'
keyword:
- Electrical and Electronic Engineering
- Atomic and Molecular Physics
- and Optics
- Electronic
- Optical and Magnetic Materials
language:
- iso: eng
page: 769-772
publication: IEEE Photonics Technology Letters
publication_identifier:
  issn:
  - 1041-1135
  - 1941-0174
publication_status: published
publisher: Institute of Electrical and Electronics Engineers (IEEE)
status: public
title: A Pulsed Lidar System With Ultimate Quantum Range Accuracy
type: journal_article
user_id: '27150'
volume: 35
year: '2023'
...