---
_id: '64877'
author:
- first_name: Behnood
  full_name: Taheri, Behnood
  last_name: Taheri
- first_name: Denis
  full_name: Kopylov, Denis
  id: '98502'
  last_name: Kopylov
- first_name: Manfred
  full_name: Hammer, Manfred
  id: '48077'
  last_name: Hammer
  orcid: 0000-0002-6331-9348
- first_name: Torsten
  full_name: Meier, Torsten
  id: '344'
  last_name: Meier
  orcid: 0000-0001-8864-2072
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
- first_name: Polina R.
  full_name: Sharapova, Polina R.
  id: '60286'
  last_name: Sharapova
citation:
  ama: Taheri B, Kopylov D, Hammer M, Meier T, Förstner J, Sharapova PR. Gain-induced
    spectral non-degeneracy in type-II parametric down-conversion. <i>arXiv</i>. Published
    online 2026. doi:<a href="https://doi.org/10.48550/ARXIV.2603.01656">10.48550/ARXIV.2603.01656</a>
  apa: Taheri, B., Kopylov, D., Hammer, M., Meier, T., Förstner, J., &#38; Sharapova,
    P. R. (2026). Gain-induced spectral non-degeneracy in type-II parametric down-conversion.
    <i>ArXiv</i>. <a href="https://doi.org/10.48550/ARXIV.2603.01656">https://doi.org/10.48550/ARXIV.2603.01656</a>
  bibtex: '@article{Taheri_Kopylov_Hammer_Meier_Förstner_Sharapova_2026, title={Gain-induced
    spectral non-degeneracy in type-II parametric down-conversion}, DOI={<a href="https://doi.org/10.48550/ARXIV.2603.01656">10.48550/ARXIV.2603.01656</a>},
    journal={arXiv}, author={Taheri, Behnood and Kopylov, Denis and Hammer, Manfred
    and Meier, Torsten and Förstner, Jens and Sharapova, Polina R.}, year={2026} }'
  chicago: Taheri, Behnood, Denis Kopylov, Manfred Hammer, Torsten Meier, Jens Förstner,
    and Polina R. Sharapova. “Gain-Induced Spectral Non-Degeneracy in Type-II Parametric
    down-Conversion.” <i>ArXiv</i>, 2026. <a href="https://doi.org/10.48550/ARXIV.2603.01656">https://doi.org/10.48550/ARXIV.2603.01656</a>.
  ieee: 'B. Taheri, D. Kopylov, M. Hammer, T. Meier, J. Förstner, and P. R. Sharapova,
    “Gain-induced spectral non-degeneracy in type-II parametric down-conversion,”
    <i>arXiv</i>, 2026, doi: <a href="https://doi.org/10.48550/ARXIV.2603.01656">10.48550/ARXIV.2603.01656</a>.'
  mla: Taheri, Behnood, et al. “Gain-Induced Spectral Non-Degeneracy in Type-II Parametric
    down-Conversion.” <i>ArXiv</i>, 2026, doi:<a href="https://doi.org/10.48550/ARXIV.2603.01656">10.48550/ARXIV.2603.01656</a>.
  short: B. Taheri, D. Kopylov, M. Hammer, T. Meier, J. Förstner, P.R. Sharapova,
    ArXiv (2026).
date_created: 2026-03-10T15:37:22Z
date_updated: 2026-03-10T15:41:18Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '35'
- _id: '34'
- _id: '61'
- _id: '230'
- _id: '623'
- _id: '429'
doi: 10.48550/ARXIV.2603.01656
language:
- iso: eng
project:
- _id: '168'
  name: TRR 142 - Polaronen-Einfluss auf die optischen Eigenschaften von Lithiumniobat
    (B07*)
- _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'
publication: arXiv
status: public
title: Gain-induced spectral non-degeneracy in type-II parametric down-conversion
type: journal_article
user_id: '16199'
year: '2026'
...
---
_id: '58544'
abstract:
- lang: eng
  text: 'We introduce a new classification of multimode states with a fixed number
    of photons. This classification is based on the factorizability of homogeneous
    multivariate polynomials and is invariant under unitary transformations. The classes
    physically correspond to field excitations in terms of single and multiple photons,
    each of which being in an arbitrary irreducible superposition of quantized modes.
    We further show how the transitions between classes are rendered possible by photon
    addition, photon subtraction, and photon-projection nonlinearities. We explicitly
    put forward a design for a multilayer interferometer in which the states for different
    classes can be generated with state-of-the-art experimental techniques. Limitations
    of the proposed designs are analyzed using the introduced classification, providing
    a benchmark for the robustness of certain states and classes. '
author:
- first_name: Denis
  full_name: Kopylov, Denis
  id: '98502'
  last_name: Kopylov
- first_name: Christian
  full_name: Offen, Christian
  id: '85279'
  last_name: Offen
  orcid: 0000-0002-5940-8057
- first_name: Laura
  full_name: Ares, Laura
  last_name: Ares
- first_name: Boris Edgar
  full_name: Wembe Moafo, Boris Edgar
  id: '95394'
  last_name: Wembe Moafo
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
- first_name: Torsten
  full_name: Meier, Torsten
  id: '344'
  last_name: Meier
  orcid: 0000-0001-8864-2072
- first_name: Polina
  full_name: Sharapova, Polina
  id: '60286'
  last_name: Sharapova
- first_name: Jan
  full_name: Sperling, Jan
  id: '75127'
  last_name: Sperling
  orcid: 0000-0002-5844-3205
citation:
  ama: Kopylov D, Offen C, Ares L, et al. Multiphoton, multimode state classification
    for nonlinear optical circuits .
  apa: Kopylov, D., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier,
    T., Sharapova, P., &#38; Sperling, J. (n.d.). <i>Multiphoton, multimode state
    classification for nonlinear optical circuits </i>.
  bibtex: '@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling,
    title={Multiphoton, multimode state classification for nonlinear optical circuits
    }, author={Kopylov, Denis and Offen, Christian and Ares, Laura and Wembe Moafo,
    Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina and
    Sperling, Jan} }'
  chicago: Kopylov, Denis, Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina
    Ober-Blöbaum, Torsten Meier, Polina Sharapova, and Jan Sperling. “Multiphoton,
    Multimode State Classification for Nonlinear Optical Circuits ,” n.d.
  ieee: D. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for
    nonlinear optical circuits .” .
  mla: Kopylov, Denis, et al. <i>Multiphoton, Multimode State Classification for Nonlinear
    Optical Circuits </i>.
  short: D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier,
    P. Sharapova, J. Sperling, (n.d.).
date_created: 2025-02-10T08:26:45Z
date_updated: 2025-02-10T08:36:12Z
department:
- _id: '623'
- _id: '15'
- _id: '636'
external_id:
  arxiv:
  - '2502.05123'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2502.05123
oa: '1'
publication_status: submitted
status: public
title: 'Multiphoton, multimode state classification for nonlinear optical circuits '
type: preprint
user_id: '85279'
year: '2025'
...
---
_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'
...