@article{65096,
  abstract     = {{<jats:p>
                    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
                    <jats:italic toggle="yes">Q</jats:italic>
                    -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.
                  </jats:p>}},
  author       = {{Folge, Patrick Fabian and Serino, Laura Maria and Mišta, Ladislav and Brecht, Benjamin and Silberhorn, Christine and Řeháček, Jaroslav and Hradil, Zdeněk}},
  issn         = {{2334-2536}},
  journal      = {{Optica}},
  number       = {{3}},
  publisher    = {{Optica Publishing Group}},
  title        = {{{Quantum-limited detection of the arrival time and the carrier frequency of time-dependent signals}}},
  doi          = {{10.1364/optica.579459}},
  volume       = {{13}},
  year         = {{2026}},
}

@article{65095,
  abstract     = {{<jats:p>
                    We provide experimental validation of tight entropic uncertainty relations for the Shannon entropies of observables with mutually unbiased eigenstates in high dimensions. In particular, we address the cases of dimensions
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                    , 4, and 5 and consider from 2 to
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                    mutually unbiased bases. The experiment is based on pulsed frequency bins measured with a multioutput quantum pulse gate, which can perform projective measurements on a complete high-dimensional basis in the time-frequency domain. Our results fit the theoretical predictions: the bound on the sum of the entropies is never violated and is saturated by the states that minimize the uncertainty relations.
                  </jats:p>}},
  author       = {{Serino, Laura Maria and Chesi, Giovanni and Brecht, Benjamin and Maccone, Lorenzo and Macchiavello, Chiara and Silberhorn, Christine}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{3}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Experimental entropic uncertainty relations in dimensions three to five}}},
  doi          = {{10.1103/f6c4-jtlc}},
  volume       = {{113}},
  year         = {{2026}},
}

@article{63213,
  abstract     = {{<jats:p>Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: Perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually unbiased bases (MUBs). Uncertainty relations derived from joint properties of the MUBs are generally assumed to be uniform, irrespective of the specific observables chosen within a set. In this work, we demonstrate instead that the uncertainty relations can depend on the choice of observables. Through both experimental observation and numerical methods, we show that selecting different sets of three MUBs in a five-dimensional quantum system results in distinct uncertainty bounds, i.e., in varying degrees of complementarity, in terms of both entropy and variance.</jats:p>}},
  author       = {{Serino, Laura Maria and Chesi, Giovanni and Brecht, Benjamin and Maccone, Lorenzo and Macchiavello, Chiara and Silberhorn, Christine}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{3}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Complementarity-based complementarity: The choice of mutually unbiased observables shapes quantum uncertainty relations}}},
  doi          = {{10.1103/v24q-sl6n}},
  volume       = {{7}},
  year         = {{2025}},
}

@article{63215,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>High-dimensional time-frequency encodings have the potential to significantly advance quantum information science; however, practical applications require precise knowledge of the encoded quantum states, which becomes increasingly challenging for larger Hilbert spaces. Self-guided tomography (SGT) has emerged as a practical and scalable technique for this purpose in the spatial domain. Here, we apply SGT to estimate time-frequency states using a multi-output quantum pulse gate. We achieve fidelities of more than 99% for 3- and 5-dimensional states without the need for calibration or post-processing. We demonstrate the robustness of SGT against statistical and environmental noise, highlighting its efficacy in the photon-starved regime typical of quantum information applications.</jats:p>}},
  author       = {{Serino, Laura Maria and Rambach, Markus and Brecht, Benjamin and Romero, Jacquiline and Silberhorn, Christine}},
  issn         = {{2058-9565}},
  journal      = {{Quantum Science and Technology}},
  number       = {{2}},
  publisher    = {{IOP Publishing}},
  title        = {{{Self-guided tomography of time-frequency qudits}}},
  doi          = {{10.1088/2058-9565/adb0ea}},
  volume       = {{10}},
  year         = {{2025}},
}

@misc{57089,
  author       = {{Kruse, Stephan and Brecht, Benjamin and Silberhorn, Christine and Serino, Laura Maria}},
  title        = {{{Quantenoptisch-unterstütztes Sende-/Empfangssystem}}},
  year         = {{2024}},
}

@article{56267,
  author       = {{Serino, Laura and Ridder, Werner and Bhattacharjee, Abhinandan and Gil López, Jano and Brecht, Benjamin and Silberhorn, Christine}},
  issn         = {{2837-6714}},
  journal      = {{Optica Quantum}},
  publisher    = {{Optica Publishing Group}},
  title        = {{{Orchestrating time and color: a programmable source of high-dimensional entanglement}}},
  doi          = {{10.1364/opticaq.532334}},
  year         = {{2024}},
}

@article{63216,
  abstract     = {{<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>}},
  author       = {{Bhattacharjee, Abhinandan and Folge, Patrick Fabian and Serino, Laura Maria and Řeháček, Jaroslav and Hradil, Zdeněk and Silberhorn, Christine and Brecht, Benjamin}},
  issn         = {{1094-4087}},
  journal      = {{Optics Express}},
  number       = {{3}},
  publisher    = {{Optica Publishing Group}},
  title        = {{{Pulse characterization at the single-photon level through chronocyclic <i>Q</i>-function measurements}}},
  doi          = {{10.1364/oe.540125}},
  volume       = {{33}},
  year         = {{2024}},
}

@article{63217,
  abstract     = {{<jats:p>We demonstrate a high-dimensional mode-sorter for single photons based on a multi-output quantum pulse gate, which we can program to switch between different temporal-mode encodings including pulse modes, frequency bins, time bins, and their superpositions. This device can facilitate practical realizations of quantum information applications such as high-dimensional quantum key distribution and thus enables secure communication with enhanced information capacity. We characterize the mode-sorter through a detector tomography in 3 and 5 dimensions and find a fidelity up to 0.958 ± 0.030 at the single-photon level.</jats:p>}},
  author       = {{Serino, Laura Maria and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}},
  issn         = {{1094-4087}},
  journal      = {{Optics Express}},
  number       = {{3}},
  publisher    = {{Optica Publishing Group}},
  title        = {{{Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate}}},
  doi          = {{10.1364/oe.544206}},
  volume       = {{33}},
  year         = {{2024}},
}

@article{45485,
  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}},
  issn         = {{1041-1135}},
  journal      = {{IEEE Photonics Technology Letters}},
  keywords     = {{Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials}},
  number       = {{14}},
  pages        = {{769--772}},
  publisher    = {{Institute of Electrical and Electronics Engineers (IEEE)}},
  title        = {{{A Pulsed Lidar System With Ultimate Quantum Range Accuracy}}},
  doi          = {{10.1109/lpt.2023.3277515}},
  volume       = {{35}},
  year         = {{2023}},
}

@article{44081,
  author       = {{Serino, Laura and Gil López, Jano and Stefszky, Michael and Ricken, Raimund and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}},
  issn         = {{2691-3399}},
  journal      = {{PRX Quantum}},
  keywords     = {{General Physics and Astronomy, Mathematical Physics, Applied Mathematics, Electronic, Optical and Magnetic Materials, Electrical and Electronic Engineering, General Computer Science}},
  number       = {{2}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States}}},
  doi          = {{10.1103/prxquantum.4.020306}},
  volume       = {{4}},
  year         = {{2023}},
}