---
_id: '63451'
abstract:
- lang: eng
  text: <jats:p>Superconducting nanowire single-photon detectors (SNSPDs) can enable
    photon-number resolution (PNR) based on accurate measurements of the detector’s
    response time to few-photon optical pulses. In this work, we investigate the impact
    of the optical pulse shape and duration on the accuracy of this method. We find
    that Gaussian temporal pulse shapes yield cleaner arrival-time histograms and,
    thus, more accurate PNR, compared to bandpass-filtered pulses of equal bandwidth.
    For low system jitter and an optical pulse duration comparable to the other jitter
    contributions, photon numbers can be discriminated in our system with a commercial
    SNSPD. At 60 ps optical pulse duration, photon-number discrimination is significantly
    reduced. Furthermore, we highlight the importance of using the correct arrival-time
    histogram model when analyzing photon-number assignment. Using exponentially modified
    Gaussian distributions, instead of the commonly used Gaussian distributions, we
    can more accurately determine photon-number misidentification probabilities. Finally,
    we reconstruct the positive operator-valued measures of the detector, revealing
    sharp features that indicate the intrinsic PNR capabilities.</jats:p>
article_number: '016102'
author:
- first_name: Timon
  full_name: Schapeler, Timon
  id: '55629'
  last_name: Schapeler
  orcid: 0000-0001-7652-1716
- first_name: Isabell
  full_name: Mischke, Isabell
  last_name: Mischke
- first_name: Fabian
  full_name: Schlue, Fabian
  id: '63579'
  last_name: Schlue
- 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
- first_name: Tim
  full_name: Bartley, Tim
  id: '49683'
  last_name: Bartley
citation:
  ama: Schapeler T, Mischke I, Schlue F, et al. Practical considerations for assignment
    of photon numbers with SNSPDs. <i>APL Quantum</i>. 2026;3(1). doi:<a href="https://doi.org/10.1063/5.0304127">10.1063/5.0304127</a>
  apa: Schapeler, T., Mischke, I., Schlue, F., Stefszky, M., Brecht, B., Silberhorn,
    C., &#38; Bartley, T. (2026). Practical considerations for assignment of photon
    numbers with SNSPDs. <i>APL Quantum</i>, <i>3</i>(1), Article 016102. <a href="https://doi.org/10.1063/5.0304127">https://doi.org/10.1063/5.0304127</a>
  bibtex: '@article{Schapeler_Mischke_Schlue_Stefszky_Brecht_Silberhorn_Bartley_2026,
    title={Practical considerations for assignment of photon numbers with SNSPDs},
    volume={3}, DOI={<a href="https://doi.org/10.1063/5.0304127">10.1063/5.0304127</a>},
    number={1016102}, journal={APL Quantum}, publisher={AIP Publishing}, author={Schapeler,
    Timon and Mischke, Isabell and Schlue, Fabian and Stefszky, Michael and Brecht,
    Benjamin and Silberhorn, Christine and Bartley, Tim}, year={2026} }'
  chicago: Schapeler, Timon, Isabell Mischke, Fabian Schlue, Michael Stefszky, Benjamin
    Brecht, Christine Silberhorn, and Tim Bartley. “Practical Considerations for Assignment
    of Photon Numbers with SNSPDs.” <i>APL Quantum</i> 3, no. 1 (2026). <a href="https://doi.org/10.1063/5.0304127">https://doi.org/10.1063/5.0304127</a>.
  ieee: 'T. Schapeler <i>et al.</i>, “Practical considerations for assignment of photon
    numbers with SNSPDs,” <i>APL Quantum</i>, vol. 3, no. 1, Art. no. 016102, 2026,
    doi: <a href="https://doi.org/10.1063/5.0304127">10.1063/5.0304127</a>.'
  mla: Schapeler, Timon, et al. “Practical Considerations for Assignment of Photon
    Numbers with SNSPDs.” <i>APL Quantum</i>, vol. 3, no. 1, 016102, AIP Publishing,
    2026, doi:<a href="https://doi.org/10.1063/5.0304127">10.1063/5.0304127</a>.
  short: T. Schapeler, I. Mischke, F. Schlue, M. Stefszky, B. Brecht, C. Silberhorn,
    T. Bartley, APL Quantum 3 (2026).
date_created: 2026-01-05T10:00:58Z
date_updated: 2026-03-25T08:00:27Z
department:
- _id: '15'
- _id: '623'
- _id: '288'
doi: 10.1063/5.0304127
intvolume: '         3'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
project:
- _id: '191'
  name: 'PhoQuant: Photonische Quantencomputer -  Quantencomputing Testplattform'
- _id: '239'
  name: 'ERC-Grant: QuESADILLA: Quantum Engineering Superconducting Array Detectors
    in Low-Light Applications'
publication: APL Quantum
publication_identifier:
  issn:
  - 2835-0103
publication_status: published
publisher: AIP Publishing
status: public
title: Practical considerations for assignment of photon numbers with SNSPDs
type: journal_article
user_id: '27150'
volume: 3
year: '2026'
...
---
_id: '63562'
abstract:
- lang: eng
  text: '<jats:p>Entangled two-mode Gaussian states constitute an important building
    block for continuous variable quantum computing and communication protocols. In
    this work, we theoretically study two-mode bipartite states, which are extracted
    from multimode light generated via type-II parametric downconversion (PDC) in
    lossy waveguides. For these states, we demonstrate that the squeezing quantifies
    entanglement and we construct a measurement basis, which results in the maximal
    bipartite entanglement. We illustrate our findings by numerically solving the
    spatial master equation for PDC in a Markovian environment. The optimal measurement
    modes are compared with two widely used broadband bases: the Mercer–Wolf basis
    (the first-order coherence basis) and the Williamson–Euler basis.</jats:p>'
article_number: '046116'
author:
- first_name: Denis
  full_name: Kopylov, Denis
  id: '98502'
  last_name: Kopylov
- first_name: Torsten
  full_name: Meier, Torsten
  id: '344'
  last_name: Meier
  orcid: 0000-0001-8864-2072
- first_name: Polina R.
  full_name: Sharapova, Polina R.
  id: '60286'
  last_name: Sharapova
citation:
  ama: Kopylov D, Meier T, Sharapova PR. Bipartite entanglement extracted from multimode
    squeezed light generated in lossy waveguides. <i>APL Quantum</i>. 2025;2(4). doi:<a
    href="https://doi.org/10.1063/5.0293116">10.1063/5.0293116</a>
  apa: Kopylov, D., Meier, T., &#38; Sharapova, P. R. (2025). Bipartite entanglement
    extracted from multimode squeezed light generated in lossy waveguides. <i>APL
    Quantum</i>, <i>2</i>(4), Article 046116. <a href="https://doi.org/10.1063/5.0293116">https://doi.org/10.1063/5.0293116</a>
  bibtex: '@article{Kopylov_Meier_Sharapova_2025, title={Bipartite entanglement extracted
    from multimode squeezed light generated in lossy waveguides}, volume={2}, DOI={<a
    href="https://doi.org/10.1063/5.0293116">10.1063/5.0293116</a>}, number={4046116},
    journal={APL Quantum}, publisher={AIP Publishing}, author={Kopylov, Denis and
    Meier, Torsten and Sharapova, Polina R.}, year={2025} }'
  chicago: Kopylov, Denis, Torsten Meier, and Polina R. Sharapova. “Bipartite Entanglement
    Extracted from Multimode Squeezed Light Generated in Lossy Waveguides.” <i>APL
    Quantum</i> 2, no. 4 (2025). <a href="https://doi.org/10.1063/5.0293116">https://doi.org/10.1063/5.0293116</a>.
  ieee: 'D. Kopylov, T. Meier, and P. R. Sharapova, “Bipartite entanglement extracted
    from multimode squeezed light generated in lossy waveguides,” <i>APL Quantum</i>,
    vol. 2, no. 4, Art. no. 046116, 2025, doi: <a href="https://doi.org/10.1063/5.0293116">10.1063/5.0293116</a>.'
  mla: Kopylov, Denis, et al. “Bipartite Entanglement Extracted from Multimode Squeezed
    Light Generated in Lossy Waveguides.” <i>APL Quantum</i>, vol. 2, no. 4, 046116,
    AIP Publishing, 2025, doi:<a href="https://doi.org/10.1063/5.0293116">10.1063/5.0293116</a>.
  short: D. Kopylov, T. Meier, P.R. Sharapova, APL Quantum 2 (2025).
date_created: 2026-01-12T13:18:51Z
date_updated: 2026-01-12T13:23:36Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '429'
- _id: '230'
- _id: '623'
- _id: '35'
doi: 10.1063/5.0293116
intvolume: '         2'
issue: '4'
language:
- iso: eng
project:
- _id: '53'
  name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
    zu funktionellen Strukturen'
- _id: '56'
  name: TRR 142 - Project Area C
- _id: '174'
  name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
    Systemen: Eine theoretische Analyse'
- _id: '266'
  name: 'PhoQC: Photonisches Quantencomputing'
publication: APL Quantum
publication_identifier:
  issn:
  - 2835-0103
publication_status: published
publisher: AIP Publishing
status: public
title: Bipartite entanglement extracted from multimode squeezed light generated in
  lossy waveguides
type: journal_article
user_id: '16199'
volume: 2
year: '2025'
...
---
_id: '61251'
abstract:
- lang: eng
  text: <jats:p>We theoretically investigate strategies for the deterministic creation
    of trains of time-bin entangled photons using an individual quantum emitter described
    by a Λ-type electronic system. We explicitly demonstrate the theoretical generation
    of linear cluster states with substantial numbers of entangled photonic qubits
    in full microscopic numerical simulations. The underlying scheme is based on the
    manipulation of ground state coherences through precise optical driving. One important
    finding is that the most easily accessible quality metrics, the achievable rotation
    fidelities, fall short in assessing the actual quantum correlations of the emitted
    photons in the face of losses. To address this, we explicitly calculate stabilizer
    generator expectation values as a superior gauge for the quantum properties of
    the generated many-photon state. With widespread applicability in other emitter
    and excitation–emission schemes also, our work lays the conceptual foundations
    for an in-depth practical analysis of time-bin entanglement based on full numerical
    simulations with predictive capabilities for realistic systems and setups, including
    losses and imperfections. The specific results shown in the present work illustrate
    that with controlled minimization of losses and realistic system parameters for
    quantum-dot type systems, useful linear cluster states of significant lengths
    can be generated in the calculations, discussing the possibility of scalability
    for quantum information processing endeavors.</jats:p>
article_number: '036110'
author:
- first_name: David
  full_name: Bauch, David
  last_name: Bauch
- first_name: Nikolas
  full_name: Köcher, Nikolas
  id: '79191'
  last_name: Köcher
- first_name: Nils
  full_name: Heinisch, Nils
  id: '90283'
  last_name: Heinisch
  orcid: 0009-0006-0984-2097
- first_name: Stefan
  full_name: Schumacher, Stefan
  id: '27271'
  last_name: Schumacher
  orcid: 0000-0003-4042-4951
citation:
  ama: Bauch D, Köcher N, Heinisch N, Schumacher S. Time-bin entanglement in the deterministic
    generation of linear photonic cluster states. <i>APL Quantum</i>. 2024;1(3). doi:<a
    href="https://doi.org/10.1063/5.0214197">10.1063/5.0214197</a>
  apa: Bauch, D., Köcher, N., Heinisch, N., &#38; Schumacher, S. (2024). Time-bin
    entanglement in the deterministic generation of linear photonic cluster states.
    <i>APL Quantum</i>, <i>1</i>(3), Article 036110. <a href="https://doi.org/10.1063/5.0214197">https://doi.org/10.1063/5.0214197</a>
  bibtex: '@article{Bauch_Köcher_Heinisch_Schumacher_2024, title={Time-bin entanglement
    in the deterministic generation of linear photonic cluster states}, volume={1},
    DOI={<a href="https://doi.org/10.1063/5.0214197">10.1063/5.0214197</a>}, number={3036110},
    journal={APL Quantum}, publisher={AIP Publishing}, author={Bauch, David and Köcher,
    Nikolas and Heinisch, Nils and Schumacher, Stefan}, year={2024} }'
  chicago: Bauch, David, Nikolas Köcher, Nils Heinisch, and Stefan Schumacher. “Time-Bin
    Entanglement in the Deterministic Generation of Linear Photonic Cluster States.”
    <i>APL Quantum</i> 1, no. 3 (2024). <a href="https://doi.org/10.1063/5.0214197">https://doi.org/10.1063/5.0214197</a>.
  ieee: 'D. Bauch, N. Köcher, N. Heinisch, and S. Schumacher, “Time-bin entanglement
    in the deterministic generation of linear photonic cluster states,” <i>APL Quantum</i>,
    vol. 1, no. 3, Art. no. 036110, 2024, doi: <a href="https://doi.org/10.1063/5.0214197">10.1063/5.0214197</a>.'
  mla: Bauch, David, et al. “Time-Bin Entanglement in the Deterministic Generation
    of Linear Photonic Cluster States.” <i>APL Quantum</i>, vol. 1, no. 3, 036110,
    AIP Publishing, 2024, doi:<a href="https://doi.org/10.1063/5.0214197">10.1063/5.0214197</a>.
  short: D. Bauch, N. Köcher, N. Heinisch, S. Schumacher, APL Quantum 1 (2024).
date_created: 2025-09-12T11:08:59Z
date_updated: 2025-09-12T11:11:32Z
department:
- _id: '15'
- _id: '170'
- _id: '297'
- _id: '35'
- _id: '230'
- _id: '27'
- _id: '429'
- _id: '623'
doi: 10.1063/5.0214197
intvolume: '         1'
issue: '3'
language:
- iso: eng
project:
- _id: '53'
  name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
    zu funktionellen Strukturen'
- _id: '56'
  name: TRR 142 - Project Area C
- _id: '173'
  name: 'TRR 142; TP C09: Ideale Erzeugung von Photonenpaaren für Verschränkungsaustausch
    bei Telekom Wellenlängen'
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '266'
  name: 'PhoQC: Photonisches Quantencomputing'
publication: APL Quantum
publication_identifier:
  issn:
  - 2835-0103
publication_status: published
publisher: AIP Publishing
status: public
title: Time-bin entanglement in the deterministic generation of linear photonic cluster
  states
type: journal_article
user_id: '16199'
volume: 1
year: '2024'
...
---
_id: '62868'
abstract:
- lang: eng
  text: <jats:p>We theoretically investigate strategies for the deterministic creation
    of trains of time-bin entangled photons using an individual quantum emitter described
    by a Λ-type electronic system. We explicitly demonstrate the theoretical generation
    of linear cluster states with substantial numbers of entangled photonic qubits
    in full microscopic numerical simulations. The underlying scheme is based on the
    manipulation of ground state coherences through precise optical driving. One important
    finding is that the most easily accessible quality metrics, the achievable rotation
    fidelities, fall short in assessing the actual quantum correlations of the emitted
    photons in the face of losses. To address this, we explicitly calculate stabilizer
    generator expectation values as a superior gauge for the quantum properties of
    the generated many-photon state. With widespread applicability in other emitter
    and excitation–emission schemes also, our work lays the conceptual foundations
    for an in-depth practical analysis of time-bin entanglement based on full numerical
    simulations with predictive capabilities for realistic systems and setups, including
    losses and imperfections. The specific results shown in the present work illustrate
    that with controlled minimization of losses and realistic system parameters for
    quantum-dot type systems, useful linear cluster states of significant lengths
    can be generated in the calculations, discussing the possibility of scalability
    for quantum information processing endeavors.</jats:p>
article_number: '036110'
author:
- first_name: David
  full_name: Bauch, David
  last_name: Bauch
- first_name: Nikolas
  full_name: Köcher, Nikolas
  id: '79191'
  last_name: Köcher
- first_name: Nils
  full_name: Heinisch, Nils
  id: '90283'
  last_name: Heinisch
  orcid: 0009-0006-0984-2097
- first_name: Stefan
  full_name: Schumacher, Stefan
  id: '27271'
  last_name: Schumacher
  orcid: 0000-0003-4042-4951
citation:
  ama: Bauch D, Köcher N, Heinisch N, Schumacher S. Time-bin entanglement in the deterministic
    generation of linear photonic cluster states. <i>APL Quantum</i>. 2024;1(3). doi:<a
    href="https://doi.org/10.1063/5.0214197">10.1063/5.0214197</a>
  apa: Bauch, D., Köcher, N., Heinisch, N., &#38; Schumacher, S. (2024). Time-bin
    entanglement in the deterministic generation of linear photonic cluster states.
    <i>APL Quantum</i>, <i>1</i>(3), Article 036110. <a href="https://doi.org/10.1063/5.0214197">https://doi.org/10.1063/5.0214197</a>
  bibtex: '@article{Bauch_Köcher_Heinisch_Schumacher_2024, title={Time-bin entanglement
    in the deterministic generation of linear photonic cluster states}, volume={1},
    DOI={<a href="https://doi.org/10.1063/5.0214197">10.1063/5.0214197</a>}, number={3036110},
    journal={APL Quantum}, publisher={AIP Publishing}, author={Bauch, David and Köcher,
    Nikolas and Heinisch, Nils and Schumacher, Stefan}, year={2024} }'
  chicago: Bauch, David, Nikolas Köcher, Nils Heinisch, and Stefan Schumacher. “Time-Bin
    Entanglement in the Deterministic Generation of Linear Photonic Cluster States.”
    <i>APL Quantum</i> 1, no. 3 (2024). <a href="https://doi.org/10.1063/5.0214197">https://doi.org/10.1063/5.0214197</a>.
  ieee: 'D. Bauch, N. Köcher, N. Heinisch, and S. Schumacher, “Time-bin entanglement
    in the deterministic generation of linear photonic cluster states,” <i>APL Quantum</i>,
    vol. 1, no. 3, Art. no. 036110, 2024, doi: <a href="https://doi.org/10.1063/5.0214197">10.1063/5.0214197</a>.'
  mla: Bauch, David, et al. “Time-Bin Entanglement in the Deterministic Generation
    of Linear Photonic Cluster States.” <i>APL Quantum</i>, vol. 1, no. 3, 036110,
    AIP Publishing, 2024, doi:<a href="https://doi.org/10.1063/5.0214197">10.1063/5.0214197</a>.
  short: D. Bauch, N. Köcher, N. Heinisch, S. Schumacher, APL Quantum 1 (2024).
date_created: 2025-12-04T12:35:53Z
date_updated: 2025-12-05T13:55:00Z
department:
- _id: '15'
- _id: '170'
- _id: '297'
- _id: '705'
- _id: '35'
- _id: '27'
- _id: '429'
- _id: '230'
- _id: '623'
doi: 10.1063/5.0214197
intvolume: '         1'
issue: '3'
language:
- iso: eng
project:
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '173'
  name: 'TRR 142; TP C09: Ideale Erzeugung von Photonenpaaren für Verschränkungsaustausch
    bei Telekom Wellenlängen'
- _id: '266'
  name: 'PhoQC: Photonisches Quantencomputing'
- _id: '53'
  name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
    zu funktionellen Strukturen'
- _id: '56'
  name: TRR 142 - Project Area C
publication: APL Quantum
publication_identifier:
  issn:
  - 2835-0103
publication_status: published
publisher: AIP Publishing
status: public
title: Time-bin entanglement in the deterministic generation of linear photonic cluster
  states
type: journal_article
user_id: '16199'
volume: 1
year: '2024'
...