---
_id: '65745'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>In this work,
    we address the numerical identification of entanglement in dynamical scenarios.
    To this end, we consider different programs based on the restriction of the evolution
    to the set of separable (i.e., non-entangled) states, together with the discretization
    of the space of variables for numerical computations. As a first approach, we
    apply linear splitting methods to the restricted, continuous equations of motion
    derived from variational principles. We utilize an exchange interaction Hamiltonian
    to confirm that the numerical and analytical solutions coincide in the limit of
    small time steps. The application to different Hamiltonians shows the wide applicability
    of the method to detect dynamical entanglement. To avoid the derivation of analytical
    solutions for complex dynamics, we consider variational, numerical integration
    schemes, introducing a variational discretization for Lagrangians linear in velocities.
    Here, we examine and compare two approaches: one in which the system is discretized
    before the restriction is applied, and another in which the restriction precedes
    the discretization. We find that the \"first-discretize-then-restrict\" method
    becomes numerically unstable, already for the example of an exchange-interaction
    Hamiltonian, which can be an important consideration for the numerical analysis
    of constrained quantum dynamics. Thereby, broadly applicable numerical tools,
    including their limitations, for studying entanglement over time are established
    for assessing the entangling power of processes that are used in quantum information
    theory.</jats:p>"
author:
- first_name: Christian
  full_name: Offen, Christian
  last_name: Offen
- first_name: Boris
  full_name: Wembe, Boris
  last_name: Wembe
- first_name: Laura
  full_name: Ares, Laura
  last_name: Ares
- first_name: Jan
  full_name: Sperling, Jan
  last_name: Sperling
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  last_name: Ober-Blöbaum
citation:
  ama: 'Offen C, Wembe B, Ares L, Sperling J, Ober-Blöbaum S. Numerical approaches
    to entangling dynamics from variational principles. <i>Journal of Physics A: Mathematical
    and Theoretical</i>. Published online 2026. doi:<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>'
  apa: 'Offen, C., Wembe, B., Ares, L., Sperling, J., &#38; Ober-Blöbaum, S. (2026).
    Numerical approaches to entangling dynamics from variational principles. <i>Journal
    of Physics A: Mathematical and Theoretical</i>. <a href="https://doi.org/10.1088/1751-8121/ae6d51">https://doi.org/10.1088/1751-8121/ae6d51</a>'
  bibtex: '@article{Offen_Wembe_Ares_Sperling_Ober-Blöbaum_2026, title={Numerical
    approaches to entangling dynamics from variational principles}, DOI={<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>},
    journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing},
    author={Offen, Christian and Wembe, Boris and Ares, Laura and Sperling, Jan and
    Ober-Blöbaum, Sina}, year={2026} }'
  chicago: 'Offen, Christian, Boris Wembe, Laura Ares, Jan Sperling, and Sina Ober-Blöbaum.
    “Numerical Approaches to Entangling Dynamics from Variational Principles.” <i>Journal
    of Physics A: Mathematical and Theoretical</i>, 2026. <a href="https://doi.org/10.1088/1751-8121/ae6d51">https://doi.org/10.1088/1751-8121/ae6d51</a>.'
  ieee: 'C. Offen, B. Wembe, L. Ares, J. Sperling, and S. Ober-Blöbaum, “Numerical
    approaches to entangling dynamics from variational principles,” <i>Journal of
    Physics A: Mathematical and Theoretical</i>, 2026, doi: <a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>.'
  mla: 'Offen, Christian, et al. “Numerical Approaches to Entangling Dynamics from
    Variational Principles.” <i>Journal of Physics A: Mathematical and Theoretical</i>,
    IOP Publishing, 2026, doi:<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>.'
  short: 'C. Offen, B. Wembe, L. Ares, J. Sperling, S. Ober-Blöbaum, Journal of Physics
    A: Mathematical and Theoretical (2026).'
date_created: 2026-06-01T09:36:09Z
date_updated: 2026-06-01T09:36:17Z
department:
- _id: '94'
doi: 10.1088/1751-8121/ae6d51
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
  issn:
  - 1751-8113
  - 1751-8121
publication_status: published
publisher: IOP Publishing
status: public
title: Numerical approaches to entangling dynamics from variational principles
type: journal_article
user_id: '95394'
year: '2026'
...
---
_id: '65742'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>In this work,
    we address the numerical identification of entanglement in dynamical scenarios.
    To this end, we consider different programs based on the restriction of the evolution
    to the set of separable (i.e., non-entangled) states, together with the discretization
    of the space of variables for numerical computations. As a first approach, we
    apply linear splitting methods to the restricted, continuous equations of motion
    derived from variational principles. We utilize an exchange interaction Hamiltonian
    to confirm that the numerical and analytical solutions coincide in the limit of
    small time steps. The application to different Hamiltonians shows the wide applicability
    of the method to detect dynamical entanglement. To avoid the derivation of analytical
    solutions for complex dynamics, we consider variational, numerical integration
    schemes, introducing a variational discretization for Lagrangians linear in velocities.
    Here, we examine and compare two approaches: one in which the system is discretized
    before the restriction is applied, and another in which the restriction precedes
    the discretization. We find that the \"first-discretize-then-restrict\" method
    becomes numerically unstable, already for the example of an exchange-interaction
    Hamiltonian, which can be an important consideration for the numerical analysis
    of constrained quantum dynamics. Thereby, broadly applicable numerical tools,
    including their limitations, for studying entanglement over time are established
    for assessing the entangling power of processes that are used in quantum information
    theory.</jats:p>"
author:
- first_name: Christian
  full_name: Offen, Christian
  last_name: Offen
- first_name: Boris
  full_name: Wembe, Boris
  last_name: Wembe
- first_name: Laura
  full_name: Ares, Laura
  last_name: Ares
- first_name: Jan
  full_name: Sperling, Jan
  last_name: Sperling
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  last_name: Ober-Blöbaum
citation:
  ama: 'Offen C, Wembe B, Ares L, Sperling J, Ober-Blöbaum S. Numerical approaches
    to entangling dynamics from variational principles. <i>Journal of Physics A: Mathematical
    and Theoretical</i>. Published online 2026. doi:<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>'
  apa: 'Offen, C., Wembe, B., Ares, L., Sperling, J., &#38; Ober-Blöbaum, S. (2026).
    Numerical approaches to entangling dynamics from variational principles. <i>Journal
    of Physics A: Mathematical and Theoretical</i>. <a href="https://doi.org/10.1088/1751-8121/ae6d51">https://doi.org/10.1088/1751-8121/ae6d51</a>'
  bibtex: '@article{Offen_Wembe_Ares_Sperling_Ober-Blöbaum_2026, title={Numerical
    approaches to entangling dynamics from variational principles}, DOI={<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>},
    journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing},
    author={Offen, Christian and Wembe, Boris and Ares, Laura and Sperling, Jan and
    Ober-Blöbaum, Sina}, year={2026} }'
  chicago: 'Offen, Christian, Boris Wembe, Laura Ares, Jan Sperling, and Sina Ober-Blöbaum.
    “Numerical Approaches to Entangling Dynamics from Variational Principles.” <i>Journal
    of Physics A: Mathematical and Theoretical</i>, 2026. <a href="https://doi.org/10.1088/1751-8121/ae6d51">https://doi.org/10.1088/1751-8121/ae6d51</a>.'
  ieee: 'C. Offen, B. Wembe, L. Ares, J. Sperling, and S. Ober-Blöbaum, “Numerical
    approaches to entangling dynamics from variational principles,” <i>Journal of
    Physics A: Mathematical and Theoretical</i>, 2026, doi: <a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>.'
  mla: 'Offen, Christian, et al. “Numerical Approaches to Entangling Dynamics from
    Variational Principles.” <i>Journal of Physics A: Mathematical and Theoretical</i>,
    IOP Publishing, 2026, doi:<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>.'
  short: 'C. Offen, B. Wembe, L. Ares, J. Sperling, S. Ober-Blöbaum, Journal of Physics
    A: Mathematical and Theoretical (2026).'
date_created: 2026-06-01T09:29:01Z
date_updated: 2026-06-01T09:29:29Z
department:
- _id: '94'
doi: 10.1088/1751-8121/ae6d51
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
  issn:
  - 1751-8113
  - 1751-8121
publication_status: published
publisher: IOP Publishing
status: public
title: Numerical approaches to entangling dynamics from variational principles
type: journal_article
user_id: '95394'
year: '2026'
...
---
_id: '65747'
abstract:
- lang: eng
  text: 'In this work, we address the numerical identification of entanglement in
    dynamical scenarios. To this end, we consider different programs based on the
    restriction of the evolution to the set of separable (i.e., non-entangled) states,
    together with the discretization of the space of variables for numerical computations.
    As a first approach, we apply linear splitting methods to the restricted, continuous
    equations of motion derived from variational principles. We utilize an exchange
    interaction Hamiltonian to confirm that the numerical and analytical solutions
    coincide in the limit of small time steps. The application to different Hamiltonians
    shows the wide applicability of the method to detect dynamical entanglement. To
    avoid the derivation of analytical solutions for complex dynamics, we consider
    variational, numerical integration schemes, introducing a variational discretization
    for Lagrangians linear in velocities. Here, we examine and compare two approaches:
    one in which the system is discretized before the restriction is applied, and
    another in which the restriction precedes the discretization. We find that the
    "first-discretize-then-restrict" method becomes numerically unstable, already
    for the example of an exchange-interaction Hamiltonian, which can be an important
    consideration for the numerical analysis of constrained quantum dynamics. Thereby,
    broadly applicable numerical tools, including their limitations, for studying
    entanglement over time are established for assessing the entangling power of processes
    that are used in quantum information theory.'
article_type: original
author:
- first_name: Christian
  full_name: Offen, Christian
  last_name: Offen
- first_name: Boris
  full_name: Wembe, Boris
  last_name: Wembe
- first_name: Laura
  full_name: Ares, Laura
  last_name: Ares
- first_name: Jan
  full_name: Sperling, Jan
  last_name: Sperling
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  last_name: Ober-Blöbaum
citation:
  ama: 'Offen C, Wembe B, Ares L, Sperling J, Ober-Blöbaum S. Numerical approaches
    to entangling dynamics from variational principles. <i>Journal of Physics A: Mathematical
    and Theoretical</i>. Published online 2026. doi:<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>'
  apa: 'Offen, C., Wembe, B., Ares, L., Sperling, J., &#38; Ober-Blöbaum, S. (2026).
    Numerical approaches to entangling dynamics from variational principles. <i>Journal
    of Physics A: Mathematical and Theoretical</i>. <a href="https://doi.org/10.1088/1751-8121/ae6d51">https://doi.org/10.1088/1751-8121/ae6d51</a>'
  bibtex: '@article{Offen_Wembe_Ares_Sperling_Ober-Blöbaum_2026, title={Numerical
    approaches to entangling dynamics from variational principles}, DOI={<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>},
    journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing},
    author={Offen, Christian and Wembe, Boris and Ares, Laura and Sperling, Jan and
    Ober-Blöbaum, Sina}, year={2026} }'
  chicago: 'Offen, Christian, Boris Wembe, Laura Ares, Jan Sperling, and Sina Ober-Blöbaum.
    “Numerical Approaches to Entangling Dynamics from Variational Principles.” <i>Journal
    of Physics A: Mathematical and Theoretical</i>, 2026. <a href="https://doi.org/10.1088/1751-8121/ae6d51">https://doi.org/10.1088/1751-8121/ae6d51</a>.'
  ieee: 'C. Offen, B. Wembe, L. Ares, J. Sperling, and S. Ober-Blöbaum, “Numerical
    approaches to entangling dynamics from variational principles,” <i>Journal of
    Physics A: Mathematical and Theoretical</i>, 2026, doi: <a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>.'
  mla: 'Offen, Christian, et al. “Numerical Approaches to Entangling Dynamics from
    Variational Principles.” <i>Journal of Physics A: Mathematical and Theoretical</i>,
    IOP Publishing, 2026, doi:<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>.'
  short: 'C. Offen, B. Wembe, L. Ares, J. Sperling, S. Ober-Blöbaum, Journal of Physics
    A: Mathematical and Theoretical (2026).'
date_created: 2026-06-01T09:41:19Z
date_updated: 2026-06-01T09:43:52Z
department:
- _id: '94'
doi: 10.1088/1751-8121/ae6d51
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
  issn:
  - 1751-8113
  - 1751-8121
publication_status: published
publisher: IOP Publishing
status: public
title: Numerical approaches to entangling dynamics from variational principles
type: journal_article
user_id: '95394'
year: '2026'
...
---
_id: '65777'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>In this work,
    we address the numerical identification of entanglement in dynamical scenarios.
    To this end, we consider different programs based on the restriction of the evolution
    to the set of separable (i.e., non-entangled) states, together with the discretization
    of the space of variables for numerical computations. As a first approach, we
    apply linear splitting methods to the restricted, continuous equations of motion
    derived from variational principles. We utilize an exchange interaction Hamiltonian
    to confirm that the numerical and analytical solutions coincide in the limit of
    small time steps. The application to different Hamiltonians shows the wide applicability
    of the method to detect dynamical entanglement. To avoid the derivation of analytical
    solutions for complex dynamics, we consider variational, numerical integration
    schemes, introducing a variational discretization for Lagrangians linear in velocities.
    Here, we examine and compare two approaches: one in which the system is discretized
    before the restriction is applied, and another in which the restriction precedes
    the discretization. We find that the ‘first-discretize-then-restrict’ method becomes
    numerically unstable, already for the example of an exchange-interaction Hamiltonian,
    which can be an important consideration for the numerical analysis of constrained
    quantum dynamics. Thereby, broadly applicable numerical tools, including their
    limitations, for studying entanglement over time are established for assessing
    the entangling power of processes that are used in quantum information theory.</jats:p>"
article_number: '225303'
author:
- first_name: Christian
  full_name: Offen, Christian
  last_name: Offen
- first_name: Boris Edgar
  full_name: Wembe Moafo, Boris Edgar
  id: '95394'
  last_name: Wembe Moafo
  orcid: 0000-0002-6085-8071
- first_name: Laura
  full_name: Ares, Laura
  last_name: Ares
- first_name: Jan
  full_name: Sperling, Jan
  id: '75127'
  last_name: Sperling
  orcid: 0000-0002-5844-3205
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
citation:
  ama: 'Offen C, Wembe Moafo BE, Ares L, Sperling J, Ober-Blöbaum S. Numerical approaches
    to entangling dynamics from variational principles. <i>Journal of Physics A: Mathematical
    and Theoretical</i>. 2026;59(22). doi:<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>'
  apa: 'Offen, C., Wembe Moafo, B. E., Ares, L., Sperling, J., &#38; Ober-Blöbaum,
    S. (2026). Numerical approaches to entangling dynamics from variational principles.
    <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>59</i>(22), Article
    225303. <a href="https://doi.org/10.1088/1751-8121/ae6d51">https://doi.org/10.1088/1751-8121/ae6d51</a>'
  bibtex: '@article{Offen_Wembe Moafo_Ares_Sperling_Ober-Blöbaum_2026, title={Numerical
    approaches to entangling dynamics from variational principles}, volume={59}, DOI={<a
    href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>},
    number={22225303}, journal={Journal of Physics A: Mathematical and Theoretical},
    publisher={IOP Publishing}, author={Offen, Christian and Wembe Moafo, Boris Edgar
    and Ares, Laura and Sperling, Jan and Ober-Blöbaum, Sina}, year={2026} }'
  chicago: 'Offen, Christian, Boris Edgar Wembe Moafo, Laura Ares, Jan Sperling, and
    Sina Ober-Blöbaum. “Numerical Approaches to Entangling Dynamics from Variational
    Principles.” <i>Journal of Physics A: Mathematical and Theoretical</i> 59, no.
    22 (2026). <a href="https://doi.org/10.1088/1751-8121/ae6d51">https://doi.org/10.1088/1751-8121/ae6d51</a>.'
  ieee: 'C. Offen, B. E. Wembe Moafo, L. Ares, J. Sperling, and S. Ober-Blöbaum, “Numerical
    approaches to entangling dynamics from variational principles,” <i>Journal of
    Physics A: Mathematical and Theoretical</i>, vol. 59, no. 22, Art. no. 225303,
    2026, doi: <a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>.'
  mla: 'Offen, Christian, et al. “Numerical Approaches to Entangling Dynamics from
    Variational Principles.” <i>Journal of Physics A: Mathematical and Theoretical</i>,
    vol. 59, no. 22, 225303, IOP Publishing, 2026, doi:<a href="https://doi.org/10.1088/1751-8121/ae6d51">10.1088/1751-8121/ae6d51</a>.'
  short: 'C. Offen, B.E. Wembe Moafo, L. Ares, J. Sperling, S. Ober-Blöbaum, Journal
    of Physics A: Mathematical and Theoretical 59 (2026).'
date_created: 2026-06-05T07:37:43Z
date_updated: 2026-06-05T07:38:44Z
department:
- _id: '623'
- _id: '15'
- _id: '170'
- _id: '706'
- _id: '429'
doi: 10.1088/1751-8121/ae6d51
intvolume: '        59'
issue: '22'
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
  issn:
  - 1751-8113
  - 1751-8121
publication_status: published
publisher: IOP Publishing
status: public
title: Numerical approaches to entangling dynamics from variational principles
type: journal_article
user_id: '75127'
volume: 59
year: '2026'
...
---
_id: '64081'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>Graph states
    are a fundamental class of multipartite entangled quantum states with wide-ranging
    applications in quantum information and computation. In this work, we develop
    a systematic approach for constructing and analyzing <jats:italic>χ</jats:italic>-colorable
    graph states, deriving explicit closed-form expressions for arbitrary <jats:italic>χ</jats:italic>.
    For a broad family of two- and three-colorable graph states, the representations
    obtained using only local operations require a minimal number of terms in the
    <jats:italic>Z</jats:italic>-eigenbasis. We prove that every two-colorable graph
    state is local Clifford (LC) equivalent to a state expressible as a summation
    of rows of an orthogonal array (OA). For graph states with <jats:italic>χ</jats:italic> &gt; 2,
    we show that they are LC-equivalent to quantum OAs, establishing a direct combinatorial
    connection between multipartite entanglement and structured quantum states. Furthermore,
    the upper and lower bounds of the Schmidt measure for graph states with arbitrary
    <jats:italic>χ</jats:italic> colorability are discussed, extending the results
    for an arbitrary local dimension. Our results offer an efficient and practical
    method for systematically constructing graph states, optimizing their representation
    in quantum circuits, and identifying structured forms of multipartite entanglement.
    This approach also connects graph states to <jats:italic>k</jats:italic>-uniform
    and absolutely maximally entangled states, motivating further exploration of the
    structure of entangled states and their applications in quantum networks, quantum
    error correction, and measurement based quantum computing.</jats:p>"
article_number: '355301'
author:
- first_name: Konstantinos-Rafail
  full_name: Revis, Konstantinos-Rafail
  last_name: Revis
- first_name: Hrachya
  full_name: Zakaryan, Hrachya
  last_name: Zakaryan
- first_name: Zahra
  full_name: Raissi, Zahra
  last_name: Raissi
citation:
  ama: 'Revis K-R, Zakaryan H, Raissi Z. χ-colorable graph states: closed-form expressions
    and quantum orthogonal arrays. <i>Journal of Physics A: Mathematical and Theoretical</i>.
    2025;58(35). doi:<a href="https://doi.org/10.1088/1751-8121/adfe45">10.1088/1751-8121/adfe45</a>'
  apa: 'Revis, K.-R., Zakaryan, H., &#38; Raissi, Z. (2025). χ-colorable graph states:
    closed-form expressions and quantum orthogonal arrays. <i>Journal of Physics A:
    Mathematical and Theoretical</i>, <i>58</i>(35), Article 355301. <a href="https://doi.org/10.1088/1751-8121/adfe45">https://doi.org/10.1088/1751-8121/adfe45</a>'
  bibtex: '@article{Revis_Zakaryan_Raissi_2025, title={χ-colorable graph states: closed-form
    expressions and quantum orthogonal arrays}, volume={58}, DOI={<a href="https://doi.org/10.1088/1751-8121/adfe45">10.1088/1751-8121/adfe45</a>},
    number={35355301}, journal={Journal of Physics A: Mathematical and Theoretical},
    publisher={IOP Publishing}, author={Revis, Konstantinos-Rafail and Zakaryan, Hrachya
    and Raissi, Zahra}, year={2025} }'
  chicago: 'Revis, Konstantinos-Rafail, Hrachya Zakaryan, and Zahra Raissi. “χ-Colorable
    Graph States: Closed-Form Expressions and Quantum Orthogonal Arrays.” <i>Journal
    of Physics A: Mathematical and Theoretical</i> 58, no. 35 (2025). <a href="https://doi.org/10.1088/1751-8121/adfe45">https://doi.org/10.1088/1751-8121/adfe45</a>.'
  ieee: 'K.-R. Revis, H. Zakaryan, and Z. Raissi, “χ-colorable graph states: closed-form
    expressions and quantum orthogonal arrays,” <i>Journal of Physics A: Mathematical
    and Theoretical</i>, vol. 58, no. 35, Art. no. 355301, 2025, doi: <a href="https://doi.org/10.1088/1751-8121/adfe45">10.1088/1751-8121/adfe45</a>.'
  mla: 'Revis, Konstantinos-Rafail, et al. “χ-Colorable Graph States: Closed-Form
    Expressions and Quantum Orthogonal Arrays.” <i>Journal of Physics A: Mathematical
    and Theoretical</i>, vol. 58, no. 35, 355301, IOP Publishing, 2025, doi:<a href="https://doi.org/10.1088/1751-8121/adfe45">10.1088/1751-8121/adfe45</a>.'
  short: 'K.-R. Revis, H. Zakaryan, Z. Raissi, Journal of Physics A: Mathematical
    and Theoretical 58 (2025).'
date_created: 2026-02-09T15:35:00Z
date_updated: 2026-02-09T17:07:25Z
ddc:
- '004'
doi: 10.1088/1751-8121/adfe45
file:
- access_level: closed
  content_type: application/pdf
  creator: zraissi
  date_created: 2026-02-09T15:35:25Z
  date_updated: 2026-02-09T15:35:25Z
  file_id: '64082'
  file_name: Revis_2025_J._Phys._A%3A_Math._Theor._58_355301.pdf
  file_size: 749441
  relation: main_file
  success: 1
file_date_updated: 2026-02-09T15:35:25Z
has_accepted_license: '1'
intvolume: '        58'
issue: '35'
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
  issn:
  - 1751-8113
  - 1751-8121
publication_status: published
publisher: IOP Publishing
status: public
title: 'χ-colorable graph states: closed-form expressions and quantum orthogonal arrays'
type: journal_article
user_id: '98836'
volume: 58
year: '2025'
...
---
_id: '64591'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>Graph states
    are a fundamental class of multipartite entangled quantum states with wide-ranging
    applications in quantum information and computation. In this work, we develop
    a systematic approach for constructing and analyzing <jats:italic>χ</jats:italic>-colorable
    graph states, deriving explicit closed-form expressions for arbitrary <jats:italic>χ</jats:italic>.
    For a broad family of two- and three-colorable graph states, the representations
    obtained using only local operations require a minimal number of terms in the
    <jats:italic>Z</jats:italic>-eigenbasis. We prove that every two-colorable graph
    state is local Clifford (LC) equivalent to a state expressible as a summation
    of rows of an orthogonal array (OA). For graph states with <jats:italic>χ</jats:italic> &gt; 2,
    we show that they are LC-equivalent to quantum OAs, establishing a direct combinatorial
    connection between multipartite entanglement and structured quantum states. Furthermore,
    the upper and lower bounds of the Schmidt measure for graph states with arbitrary
    <jats:italic>χ</jats:italic> colorability are discussed, extending the results
    for an arbitrary local dimension. Our results offer an efficient and practical
    method for systematically constructing graph states, optimizing their representation
    in quantum circuits, and identifying structured forms of multipartite entanglement.
    This approach also connects graph states to <jats:italic>k</jats:italic>-uniform
    and absolutely maximally entangled states, motivating further exploration of the
    structure of entangled states and their applications in quantum networks, quantum
    error correction, and measurement based quantum computing.</jats:p>"
article_number: '355301'
author:
- first_name: Konstantinos-Rafail
  full_name: Revis, Konstantinos-Rafail
  last_name: Revis
- first_name: Hrachya
  full_name: Zakaryan, Hrachya
  last_name: Zakaryan
- first_name: Zahra
  full_name: Raissi, Zahra
  last_name: Raissi
citation:
  ama: 'Revis K-R, Zakaryan H, Raissi Z. <i>χ</i>-colorable graph states: closed-form
    expressions and quantum orthogonal arrays. <i>Journal of Physics A: Mathematical
    and Theoretical</i>. 2025;58(35). doi:<a href="https://doi.org/10.1088/1751-8121/adfe45">10.1088/1751-8121/adfe45</a>'
  apa: 'Revis, K.-R., Zakaryan, H., &#38; Raissi, Z. (2025). <i>χ</i>-colorable graph
    states: closed-form expressions and quantum orthogonal arrays. <i>Journal of Physics
    A: Mathematical and Theoretical</i>, <i>58</i>(35), Article 355301. <a href="https://doi.org/10.1088/1751-8121/adfe45">https://doi.org/10.1088/1751-8121/adfe45</a>'
  bibtex: '@article{Revis_Zakaryan_Raissi_2025, title={<i>χ</i>-colorable graph states:
    closed-form expressions and quantum orthogonal arrays}, volume={58}, DOI={<a href="https://doi.org/10.1088/1751-8121/adfe45">10.1088/1751-8121/adfe45</a>},
    number={35355301}, journal={Journal of Physics A: Mathematical and Theoretical},
    publisher={IOP Publishing}, author={Revis, Konstantinos-Rafail and Zakaryan, Hrachya
    and Raissi, Zahra}, year={2025} }'
  chicago: 'Revis, Konstantinos-Rafail, Hrachya Zakaryan, and Zahra Raissi. “<i>χ</i>-Colorable
    Graph States: Closed-Form Expressions and Quantum Orthogonal Arrays.” <i>Journal
    of Physics A: Mathematical and Theoretical</i> 58, no. 35 (2025). <a href="https://doi.org/10.1088/1751-8121/adfe45">https://doi.org/10.1088/1751-8121/adfe45</a>.'
  ieee: 'K.-R. Revis, H. Zakaryan, and Z. Raissi, “<i>χ</i>-colorable graph states:
    closed-form expressions and quantum orthogonal arrays,” <i>Journal of Physics
    A: Mathematical and Theoretical</i>, vol. 58, no. 35, Art. no. 355301, 2025, doi:
    <a href="https://doi.org/10.1088/1751-8121/adfe45">10.1088/1751-8121/adfe45</a>.'
  mla: 'Revis, Konstantinos-Rafail, et al. “<i>χ</i>-Colorable Graph States: Closed-Form
    Expressions and Quantum Orthogonal Arrays.” <i>Journal of Physics A: Mathematical
    and Theoretical</i>, vol. 58, no. 35, 355301, IOP Publishing, 2025, doi:<a href="https://doi.org/10.1088/1751-8121/adfe45">10.1088/1751-8121/adfe45</a>.'
  short: 'K.-R. Revis, H. Zakaryan, Z. Raissi, Journal of Physics A: Mathematical
    and Theoretical 58 (2025).'
date_created: 2026-02-23T13:32:33Z
date_updated: 2026-02-23T13:33:28Z
ddc:
- '000'
doi: 10.1088/1751-8121/adfe45
file:
- access_level: closed
  content_type: application/pdf
  creator: zraissi
  date_created: 2026-02-23T13:33:12Z
  date_updated: 2026-02-23T13:33:12Z
  file_id: '64592'
  file_name: Revis_2025_J._Phys._A%3A_Math._Theor._58_355301.pdf
  file_size: 749401
  relation: main_file
  success: 1
file_date_updated: 2026-02-23T13:33:12Z
has_accepted_license: '1'
intvolume: '        58'
issue: '35'
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
  issn:
  - 1751-8113
  - 1751-8121
publication_status: published
publisher: IOP Publishing
status: public
title: '<i>χ</i>-colorable graph states: closed-form expressions and quantum orthogonal
  arrays'
type: journal_article
user_id: '98836'
volume: 58
year: '2025'
...
---
_id: '55527'
article_number: '075301'
author:
- first_name: Zahra
  full_name: Raissi, Zahra
  id: '98836'
  last_name: Raissi
  orcid: 0000-0002-9168-8212
- first_name: Christian
  full_name: Gogolin, Christian
  last_name: Gogolin
- first_name: Arnau
  full_name: Riera, Arnau
  last_name: Riera
- first_name: Antonio
  full_name: Acín, Antonio
  last_name: Acín
citation:
  ama: 'Raissi Z, Gogolin C, Riera A, Acín A. Optimal quantum error correcting codes
    from absolutely maximally entangled states. <i>Journal of Physics A: Mathematical
    and Theoretical</i>. 2017;51(7). doi:<a href="https://doi.org/10.1088/1751-8121/aaa151">10.1088/1751-8121/aaa151</a>'
  apa: 'Raissi, Z., Gogolin, C., Riera, A., &#38; Acín, A. (2017). Optimal quantum
    error correcting codes from absolutely maximally entangled states. <i>Journal
    of Physics A: Mathematical and Theoretical</i>, <i>51</i>(7), Article 075301.
    <a href="https://doi.org/10.1088/1751-8121/aaa151">https://doi.org/10.1088/1751-8121/aaa151</a>'
  bibtex: '@article{Raissi_Gogolin_Riera_Acín_2017, title={Optimal quantum error correcting
    codes from absolutely maximally entangled states}, volume={51}, DOI={<a href="https://doi.org/10.1088/1751-8121/aaa151">10.1088/1751-8121/aaa151</a>},
    number={7075301}, journal={Journal of Physics A: Mathematical and Theoretical},
    publisher={IOP Publishing}, author={Raissi, Zahra and Gogolin, Christian and Riera,
    Arnau and Acín, Antonio}, year={2017} }'
  chicago: 'Raissi, Zahra, Christian Gogolin, Arnau Riera, and Antonio Acín. “Optimal
    Quantum Error Correcting Codes from Absolutely Maximally Entangled States.” <i>Journal
    of Physics A: Mathematical and Theoretical</i> 51, no. 7 (2017). <a href="https://doi.org/10.1088/1751-8121/aaa151">https://doi.org/10.1088/1751-8121/aaa151</a>.'
  ieee: 'Z. Raissi, C. Gogolin, A. Riera, and A. Acín, “Optimal quantum error correcting
    codes from absolutely maximally entangled states,” <i>Journal of Physics A: Mathematical
    and Theoretical</i>, vol. 51, no. 7, Art. no. 075301, 2017, doi: <a href="https://doi.org/10.1088/1751-8121/aaa151">10.1088/1751-8121/aaa151</a>.'
  mla: 'Raissi, Zahra, et al. “Optimal Quantum Error Correcting Codes from Absolutely
    Maximally Entangled States.” <i>Journal of Physics A: Mathematical and Theoretical</i>,
    vol. 51, no. 7, 075301, IOP Publishing, 2017, doi:<a href="https://doi.org/10.1088/1751-8121/aaa151">10.1088/1751-8121/aaa151</a>.'
  short: 'Z. Raissi, C. Gogolin, A. Riera, A. Acín, Journal of Physics A: Mathematical
    and Theoretical 51 (2017).'
date_created: 2024-08-05T14:45:14Z
date_updated: 2024-08-07T12:13:45Z
doi: 10.1088/1751-8121/aaa151
intvolume: '        51'
issue: '7'
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
  issn:
  - 1751-8113
  - 1751-8121
publication_status: published
publisher: IOP Publishing
status: public
title: Optimal quantum error correcting codes from absolutely maximally entangled
  states
type: journal_article
user_id: '98836'
volume: 51
year: '2017'
...
