[{"year":"2025","issue":"35","title":"χ-colorable graph states: closed-form expressions and quantum orthogonal arrays","date_created":"2026-02-09T15:35:00Z","publisher":"IOP Publishing","file":[{"file_size":749441,"file_name":"Revis_2025_J._Phys._A%3A_Math._Theor._58_355301.pdf","file_id":"64082","access_level":"closed","date_updated":"2026-02-09T15:35:25Z","creator":"zraissi","date_created":"2026-02-09T15:35:25Z","success":1,"relation":"main_file","content_type":"application/pdf"}],"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>"}],"publication":"Journal of Physics A: Mathematical and Theoretical","language":[{"iso":"eng"}],"ddc":["004"],"citation":{"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>.","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} }","short":"K.-R. Revis, H. Zakaryan, Z. Raissi, Journal of Physics A: Mathematical and Theoretical 58 (2025).","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>","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>","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>.","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>."},"intvolume":"        58","publication_status":"published","publication_identifier":{"issn":["1751-8113","1751-8121"]},"has_accepted_license":"1","doi":"10.1088/1751-8121/adfe45","author":[{"last_name":"Revis","full_name":"Revis, Konstantinos-Rafail","first_name":"Konstantinos-Rafail"},{"full_name":"Zakaryan, Hrachya","last_name":"Zakaryan","first_name":"Hrachya"},{"last_name":"Raissi","full_name":"Raissi, Zahra","first_name":"Zahra"}],"volume":58,"date_updated":"2026-02-09T17:07:25Z","status":"public","type":"journal_article","file_date_updated":"2026-02-09T15:35:25Z","article_number":"355301","user_id":"98836","_id":"64081"},{"language":[{"iso":"eng"}],"ddc":["000"],"publication":"Journal of Physics A: Mathematical and Theoretical","file":[{"date_updated":"2026-02-23T13:33:12Z","date_created":"2026-02-23T13:33:12Z","creator":"zraissi","file_size":749401,"file_id":"64592","file_name":"Revis_2025_J._Phys._A%3A_Math._Theor._58_355301.pdf","access_level":"closed","content_type":"application/pdf","success":1,"relation":"main_file"}],"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>"}],"date_created":"2026-02-23T13:32:33Z","publisher":"IOP Publishing","title":"<i>χ</i>-colorable graph states: closed-form expressions and quantum orthogonal arrays","issue":"35","year":"2025","user_id":"98836","_id":"64591","file_date_updated":"2026-02-23T13:33:12Z","article_number":"355301","type":"journal_article","status":"public","volume":58,"author":[{"first_name":"Konstantinos-Rafail","full_name":"Revis, Konstantinos-Rafail","last_name":"Revis"},{"last_name":"Zakaryan","full_name":"Zakaryan, Hrachya","first_name":"Hrachya"},{"full_name":"Raissi, Zahra","last_name":"Raissi","first_name":"Zahra"}],"date_updated":"2026-02-23T13:33:28Z","doi":"10.1088/1751-8121/adfe45","has_accepted_license":"1","publication_identifier":{"issn":["1751-8113","1751-8121"]},"publication_status":"published","intvolume":"        58","citation":{"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>.","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>.","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>","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>.","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} }","short":"K.-R. Revis, H. Zakaryan, Z. Raissi, Journal of Physics A: Mathematical and Theoretical 58 (2025).","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>"}},{"doi":"10.1088/1751-8121/aaa151","title":"Optimal quantum error correcting codes from absolutely maximally entangled states","volume":51,"date_created":"2024-08-05T14:45:14Z","author":[{"orcid":"0000-0002-9168-8212","last_name":"Raissi","full_name":"Raissi, Zahra","id":"98836","first_name":"Zahra"},{"last_name":"Gogolin","full_name":"Gogolin, Christian","first_name":"Christian"},{"full_name":"Riera, Arnau","last_name":"Riera","first_name":"Arnau"},{"last_name":"Acín","full_name":"Acín, Antonio","first_name":"Antonio"}],"date_updated":"2024-08-07T12:13:45Z","publisher":"IOP Publishing","intvolume":"        51","citation":{"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>.","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>.","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} }","short":"Z. Raissi, C. Gogolin, A. Riera, A. Acín, Journal of Physics A: Mathematical and Theoretical 51 (2017).","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>."},"year":"2017","issue":"7","publication_identifier":{"issn":["1751-8113","1751-8121"]},"publication_status":"published","language":[{"iso":"eng"}],"article_number":"075301","user_id":"98836","_id":"55527","status":"public","publication":"Journal of Physics A: Mathematical and Theoretical","type":"journal_article"}]