@article{63219,
  abstract     = {{<jats:p>We introduce the framework of Bayesian relative belief that directly evaluates whether or not the experimental data at hand support a given hypothesis regarding a quantum system by directly comparing the prior and posterior probabilities for the hypothesis. In model-dimension certification tasks, we show that the relative-belief procedure typically chooses Hilbert spaces that are never smaller in dimension than those selected from optimizing a broad class of information criteria, including Akaike's criterion. As a concrete and focused exposition of this powerful evidence-based technique, we apply the relative-belief procedure to an important application: . In particular, just by comparing prior and posterior probabilities based on data, we demonstrate its capability of tracking multiphoton emissions using (realistically lossy) single-photon detectors in order to assess the actual quality of photon sources without making  assumptions, thereby reliably safeguarding source integrity for general quantum-information and communication tasks with Bayesian reasoning. Finally, we discuss how relative belief can be exploited to carry out parametric model certification and estimate the total dimension of the quantum state for the combined (measured) physical and interacting external systems described by the Tavis-Cummings model.</jats:p>
          <jats:sec>
            <jats:title/>
            <jats:supplementary-material>
              <jats:permissions>
                <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement>
                <jats:copyright-year>2024</jats:copyright-year>
              </jats:permissions>
            </jats:supplementary-material>
          </jats:sec>}},
  author       = {{Teo, Y. S. and Shringarpure, S. U. and Jeong, H. and Prasannan, Nidhin and Brecht, Benjamin and Silberhorn, Christine and Evans, M. and Mogilevtsev, D. and Sánchez-Soto, L. L.}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Relative-belief inference in quantum information theory}}},
  doi          = {{10.1103/physreva.110.012231}},
  volume       = {{110}},
  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{63220,
  abstract     = {{<jats:p>Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and continuous variables that is fully evidence based, relying solely on the experimental data collected and no other unjustified assumptions whatsoever. Using the Bayesian concept of relative belief, we take the effective dimension of the state as the smallest one such that the posterior probability is larger than the prior, as dictated by the data. The posterior probabilities associated with the relative-belief ratios measure the strength of the evidence provide by these ratios so that we can assess whether there is weak or strong evidence in favor or against a particular dimension. Using experimental data from spectral-temporal and polarimetry measurements, we demonstrate how to correctly assign Bayesian plausible error bars for the obtained effective dimensions. This makes relative belief a conservative and easy-to-use model-selection method for any experiment.</jats:p>
          <jats:sec>
            <jats:title/>
            <jats:supplementary-material>
              <jats:permissions>
                <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement>
                <jats:copyright-year>2024</jats:copyright-year>
              </jats:permissions>
            </jats:supplementary-material>
          </jats:sec>}},
  author       = {{Teo, Y. S. and Shringarpure, S. U. and Jeong, H. and Prasannan, Nidhin and Brecht, Benjamin and Silberhorn, Christine and Evans, M. and Mogilevtsev, D. and Sánchez-Soto, L. L.}},
  issn         = {{0031-9007}},
  journal      = {{Physical Review Letters}},
  number       = {{5}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Evidence-Based Certification of Quantum Dimensions}}},
  doi          = {{10.1103/physrevlett.133.050204}},
  volume       = {{133}},
  year         = {{2024}},
}

@article{54288,
  abstract     = {{<jats:p>The ability to apply user-chosen large-scale unitary operations with high fidelity to a quantum state is key to realizing future photonic quantum technologies. Here, we realize the implementation of programmable unitary operations on up to 64 frequency-bin modes. To benchmark the performance of our system, we probe different quantum walk unitary operations, in particular, Grover walks on four-dimensional hypercubes with similarities exceeding 95% and quantum walks with 400 steps on circles and finite lines with similarities of 98%. Our results open a path toward implementing high-quality unitary operations, which can form the basis for applications in complex tasks, such as Gaussian boson sampling.</jats:p>
          <jats:sec>
            <jats:title/>
            <jats:supplementary-material>
              <jats:permissions>
                <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement>
                <jats:copyright-year>2024</jats:copyright-year>
              </jats:permissions>
            </jats:supplementary-material>
          </jats:sec>}},
  author       = {{De, Syamsundar and Ansari, Vahid and Sperling, Jan and Barkhofen, Sonja and Brecht, Benjamin and Silberhorn, Christine}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{2}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Realization of high-fidelity unitary operations on up to 64 frequency bins}}},
  doi          = {{10.1103/physrevresearch.6.l022040}},
  volume       = {{6}},
  year         = {{2024}},
}

@article{63218,
  abstract     = {{<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>
          <jats:sec>
            <jats:title/>
            <jats:supplementary-material>
              <jats:permissions>
                <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement>
                <jats:copyright-year>2024</jats:copyright-year>
              </jats:permissions>
            </jats:supplementary-material>
          </jats:sec>}},
  author       = {{Folge, Patrick Fabian and Stefszky, Michael and Brecht, Benjamin and Silberhorn, Christine}},
  issn         = {{2691-3399}},
  journal      = {{PRX Quantum}},
  number       = {{4}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates}}},
  doi          = {{10.1103/prxquantum.5.040329}},
  volume       = {{5}},
  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{54815,
  abstract     = {{<jats:p>Broadband quantum light is a vital resource for quantum metrology and spectroscopy applications such as quantum optical coherence tomography or entangled two photon absorption. For entangled two photon absorption in particular, very high photon flux combined with high time-frequency entanglement is crucial for observing a signal. So far these conditions could be met by using high power lasers driving degenerate, type 0 bulk-crystal spontaneous parametric down conversion (SPDC) sources. This naturally limits the available wavelength ranges and precludes deterministic splitting of the generated output photons. In this work we demonstrate an integrated two-colour SPDC source utilising a group-velocity matched lithium niobate waveguide, reaching both exceptional brightness 1.52⋅10<jats:sup>6</jats:sup>pairssmWGHz and large bandwidth (7.8 THz FWHM) while pumped with a few mW of continuous wave (CW) laser light. By converting a narrow band pump to broadband pulses the created photon pairs show correlation times of Δ<jats:italic>τ</jats:italic> ≈ 120 fs while maintaining the narrow bandwidth Δ<jats:italic>ω</jats:italic><jats:sub>
      <jats:italic>p</jats:italic>
    </jats:sub> ≪ 1 MHz of the CW pump light, yielding strong time-frequency entanglement. Furthermore our process can be adapted to a wide range of central wavelengths.</jats:p>}},
  author       = {{Pollmann, René and Roeder, Franz and Quiring, Victor and Ricken, Raimund and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}},
  issn         = {{1094-4087}},
  journal      = {{Optics Express}},
  number       = {{14}},
  publisher    = {{Optica Publishing Group}},
  title        = {{{Integrated, bright broadband, two-colour parametric down-conversion source}}},
  doi          = {{10.1364/oe.522549}},
  volume       = {{32}},
  year         = {{2024}},
}

@article{57862,
  abstract     = {{The latest applications in ultrafast quantum metrology require bright, broadband bi-photon sources with one of the photons in the mid-infrared and the other in the visible to near infrared. However, existing sources based on bulk crystals are limited in brightness due to the short interaction length and only allow for limited dispersion engineering. Here, we present an integrated PDC source based on a Ti:LiNbO3 waveguide that generates broadband bi-photons with central wavelengths at 860 nm and 2800 nm. Their spectral bandwidth exceeds 25 THz and is achieved by simultaneous matching of the group velocities (GVs) and cancellation of GV dispersion for the signal and idler field. We provide an intuitive understanding of the process by studying our source’s behavior at different temperatures and pump wavelengths, which agrees well with simulations.}},
  author       = {{Roeder, Franz and Gnanavel, Abira and Pollmann, René and Brecht, Olga and Stefszky, Michael and Padberg, Laura and Eigner, Christof and Silberhorn, Christine and Brecht, Benjamin}},
  issn         = {{1367-2630}},
  journal      = {{New Journal of Physics}},
  number       = {{12}},
  publisher    = {{IOP Publishing}},
  title        = {{{Ultra-broadband non-degenerate guided-wave bi-photon source in the near and mid-infrared}}},
  doi          = {{10.1088/1367-2630/ad9f98}},
  volume       = {{26}},
  year         = {{2024}},
}

@article{42158,
  author       = {{Lüders, Carolin and Gil-Lopez, Jano and Allgaier, Markus and Brecht, Benjamin and Aßmann, Marc and Silberhorn, Christine and Bayer, Manfred}},
  issn         = {{2331-7019}},
  journal      = {{Physical Review Applied}},
  keywords     = {{General Physics and Astronomy}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Tailored Frequency Conversion Makes Infrared Light Visible for Streak Cameras}}},
  doi          = {{10.1103/physrevapplied.19.014072}},
  volume       = {{19}},
  year         = {{2023}},
}

@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{45850,
  abstract     = {{Interference between single photons is key for many quantum optics experiments and applications in quantum technologies, such as quantum communication or computation. It is advantageous to operate the systems at telecommunication wavelengths and to integrate the setups for these applications in order to improve stability, compactness and scalability. A new promising material platform for integrated quantum optics is lithium niobate on insulator (LNOI). Here, we realise Hong-Ou-Mandel (HOM) interference between telecom photons from an engineered parametric down-conversion source in an LNOI directional coupler. The coupler has been designed and fabricated in house and provides close to perfect balanced beam splitting. We obtain a raw HOM visibility of (93.5 ± 0.7) %, limited mainly by the source performance and in good agreement with off-chip measurements. This lays the foundation for more sophisticated quantum experiments in LNOI.}},
  author       = {{Babel, Silia and Bollmers, Laura and Massaro, Marcello and Luo, Kai Hong and Stefszky, Michael and Pegoraro, Federico and Held, Philip and Herrmann, Harald and Eigner, Christof and Brecht, Benjamin and Padberg, Laura and Silberhorn, Christine}},
  issn         = {{1094-4087}},
  journal      = {{Optics Express}},
  keywords     = {{Atomic and Molecular Physics, and Optics}},
  number       = {{14}},
  publisher    = {{Optica Publishing Group}},
  title        = {{{Demonstration of Hong-Ou-Mandel interference in an LNOI directional coupler}}},
  doi          = {{10.1364/oe.484126}},
  volume       = {{31}},
  year         = {{2023}},
}

@article{38541,
  author       = {{Barkhofen, Sonja and Brecht, Benjamin and Silberhorn, Christine}},
  journal      = {{Physik in unserer Zeit}},
  number       = {{1}},
  pages        = {{10--11}},
  publisher    = {{Wiley}},
  title        = {{{Verschränkung wie am Fließband}}},
  doi          = {{https://doi.org/10.1002/piuz.202370107}},
  volume       = {{54}},
  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}},
}

@article{42648,
  abstract     = {{In real photonic quantum systems losses are an unavoidable factor limiting the scalability to many modes and particles, restraining their application in fields as quantum information and communication. For this reason, a considerable amount of engineering effort has been taken in order to improve the quality of particle sources and system components. At the same time, data analysis and collection methods based on post-selection have been used to mitigate the effect of particle losses. This has allowed for investigating experimentally multi-particle evolutions where the observer lacks knowledge about the system's intermediate propagation states. Nonetheless, the fundamental question how losses affect the behaviour of the surviving subset of a multi-particle system has not been investigated so far. For this reason, here we study the impact of particle losses in a quantum walk of two photons reconstructing the output probability distributions for one photon conditioned on the loss of the other in a known mode and temporal step of our evolution network. We present the underlying theoretical scheme that we have devised in order to model controlled particle losses, we describe an experimental platform capable of implementing our theory in a time multiplexing encoding. In the end we show how localized particle losses change the output distributions without altering their asymptotic spreading properties. Finally we devise a quantum civilization problem, a two walker generalisation of single particle recurrence processes.}},
  author       = {{Pegoraro, Federico and Held, Philip and Barkhofen, Sonja and Brecht, Benjamin and Silberhorn, Christine}},
  issn         = {{0031-8949}},
  journal      = {{Physica Scripta}},
  number       = {{3}},
  publisher    = {{IOP Publishing}},
  title        = {{{Dynamic conditioning of two particle discrete-time quantum walks}}},
  doi          = {{10.1088/1402-4896/acbcaa}},
  volume       = {{98}},
  year         = {{2023}},
}

@article{39025,
  author       = {{Meyer-Scott, Evan and Prasannan, Nidhin and Dhand, Ish and Eigner, Christof and Quiring, Viktor and Barkhofen, Sonja and Brecht, Benjamin and Plenio, Martin B. and Silberhorn, Christine}},
  issn         = {{0031-9007}},
  journal      = {{Physical Review Letters}},
  keywords     = {{General Physics and Astronomy}},
  number       = {{15}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Scalable Generation of Multiphoton Entangled States by Active Feed-Forward and Multiplexing}}},
  doi          = {{10.1103/physrevlett.129.150501}},
  volume       = {{129}},
  year         = {{2022}},
}

@article{40273,
  author       = {{Meyer-Scott, Evan and Prasannan, Nidhin and Dhand, Ish and Eigner, Christof and Quiring, Viktor and Barkhofen, Sonja and Brecht, Benjamin and Plenio, Martin B. and Silberhorn, Christine}},
  issn         = {{0031-9007}},
  journal      = {{Physical Review Letters}},
  keywords     = {{General Physics and Astronomy}},
  number       = {{15}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Scalable Generation of Multiphoton Entangled States by Active Feed-Forward and Multiplexing}}},
  doi          = {{10.1103/physrevlett.129.150501}},
  volume       = {{129}},
  year         = {{2022}},
}

@article{34884,
  author       = {{Prasannan, Nidhin and Sperling, Jan and Brecht, Benjamin and Silberhorn, Christine}},
  issn         = {{0031-9007}},
  journal      = {{Physical Review Letters}},
  keywords     = {{General Physics and Astronomy}},
  number       = {{26}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Direct Measurement of Higher-Order Nonlinear Polarization Squeezing}}},
  doi          = {{10.1103/physrevlett.129.263601}},
  volume       = {{129}},
  year         = {{2022}},
}

@article{29524,
  author       = {{De, Syamsundar and Gil López, Jano and Brecht, Benjamin and Silberhorn, Christine and Sánchez-Soto, Luis L. and Hradil, Zdeněk and Řeháček, Jaroslav}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  keywords     = {{General Engineering}},
  number       = {{3}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Effects of coherence on temporal resolution}}},
  doi          = {{10.1103/physrevresearch.3.033082}},
  volume       = {{3}},
  year         = {{2021}},
}

@article{21020,
  author       = {{Ansari, Vahid and Brecht, Benjamin and Gil-Lopez, Jano and Donohue, John M. and Řeháček, Jaroslav and Hradil, Zdeněk and Sánchez-Soto, Luis L. and Silberhorn, Christine}},
  issn         = {{2691-3399}},
  journal      = {{PRX Quantum}},
  title        = {{{Achieving the Ultimate Quantum Timing Resolution}}},
  doi          = {{10.1103/prxquantum.2.010301}},
  volume       = {{2}},
  year         = {{2021}},
}

@article{22259,
  author       = {{Roman-Rodriguez, V and Brecht, Benjamin and Srinivasan, K and Silberhorn, Christine and Treps, N and Diamanti, E and Parigi, V}},
  issn         = {{1367-2630}},
  journal      = {{New Journal of Physics}},
  title        = {{{Continuous variable multimode quantum states via symmetric group velocity matching}}},
  doi          = {{10.1088/1367-2630/abef96}},
  volume       = {{23}},
  year         = {{2021}},
}

