---
_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'
...