[{"abstract":[{"text":"Non-symmetric GHZ states ($n$-GHZ$_\\alpha$), characterized by unequal\r\nsuperpositions of $|00...0>$ and $|11...1>$, represent a significant yet\r\nunderexplored class of multipartite entangled states with potential\r\napplications in quantum information. Despite their importance, the lack of a\r\nwell-defined stabilizer formalism and corresponding graph representation has\r\nhindered their comprehensive study. In this paper, we address this gap by\r\nintroducing two novel graph formalisms and stabilizers for non-symmetric GHZ\r\nstates. First, we provide a weighted hypergraph representation and demonstrate\r\nthat non-symmetric GHZ states are local unitary (LU) equivalent to fully\r\nconnected weighted hypergraphs. Although these weighted hypergraphs are not\r\nstabilizer states, we show that they can be stabilized using local operations,\r\nand an ancilla. We further extend this framework to qudits, offering a specific\r\nform for non-symmetric qudit GHZ states and their LU equivalent weighted qudit\r\nhypergraphs. Second, we propose a graph formalism using controlled-unitary (CU)\r\noperations, showing that non-symmetric qudit GHZ states can be described using\r\nstar-shaped CU graphs. Our findings enhance the understanding of non-symmetric\r\nGHZ states and their potential applications in quantum information science.","lang":"eng"}],"citation":{"chicago":"Zakaryan, Hrachya, Konstantinos-Rafail Revis, and Zahra Raissi. “Non-Symmetric GHZ States; Weighted Hypergraph and Controlled-Unitary  Graph Representations.” <i>ArXiv:2408.02740</i>, 2024.","short":"H. Zakaryan, K.-R. Revis, Z. Raissi, ArXiv:2408.02740 (2024).","apa":"Zakaryan, H., Revis, K.-R., &#38; Raissi, Z. (2024). Non-symmetric GHZ states; weighted hypergraph and controlled-unitary  graph representations. In <i>arXiv:2408.02740</i>.","ieee":"H. Zakaryan, K.-R. Revis, and Z. Raissi, “Non-symmetric GHZ states; weighted hypergraph and controlled-unitary  graph representations,” <i>arXiv:2408.02740</i>. 2024.","ama":"Zakaryan H, Revis K-R, Raissi Z. Non-symmetric GHZ states; weighted hypergraph and controlled-unitary  graph representations. <i>arXiv:240802740</i>. Published online 2024.","bibtex":"@article{Zakaryan_Revis_Raissi_2024, title={Non-symmetric GHZ states; weighted hypergraph and controlled-unitary  graph representations}, journal={arXiv:2408.02740}, author={Zakaryan, Hrachya and Revis, Konstantinos-Rafail and Raissi, Zahra}, year={2024} }","mla":"Zakaryan, Hrachya, et al. “Non-Symmetric GHZ States; Weighted Hypergraph and Controlled-Unitary  Graph Representations.” <i>ArXiv:2408.02740</i>, 2024."},"publication":"arXiv:2408.02740","type":"preprint","date_created":"2024-08-07T12:04:50Z","external_id":{"arxiv":["2408.02740"]},"date_updated":"2024-08-07T12:05:19Z","author":[{"last_name":"Zakaryan","first_name":"Hrachya","full_name":"Zakaryan, Hrachya"},{"last_name":"Revis","first_name":"Konstantinos-Rafail","full_name":"Revis, Konstantinos-Rafail"},{"full_name":"Raissi, Zahra","last_name":"Raissi","orcid":"0000-0002-9168-8212","first_name":"Zahra","id":"98836"}],"year":"2024","title":"Non-symmetric GHZ states; weighted hypergraph and controlled-unitary  graph representations","status":"public","user_id":"98836","language":[{"iso":"eng"}],"_id":"55560"},{"date_created":"2024-08-20T07:18:02Z","external_id":{"arxiv":["2408.09515"]},"type":"preprint","citation":{"apa":"Revis, K.-R., Zakaryan, H., &#38; Raissi, Z. (2024). Closed-Form Expressions for Two- and Three-Colorable States. In <i>arXiv:2408.09515</i>.","ieee":"K.-R. Revis, H. Zakaryan, and Z. Raissi, “Closed-Form Expressions for Two- and Three-Colorable States,” <i>arXiv:2408.09515</i>. 2024.","chicago":"Revis, Konstantinos-Rafail, Hrachya Zakaryan, and Zahra Raissi. “Closed-Form Expressions for Two- and Three-Colorable States.” <i>ArXiv:2408.09515</i>, 2024.","short":"K.-R. Revis, H. Zakaryan, Z. Raissi, ArXiv:2408.09515 (2024).","mla":"Revis, Konstantinos-Rafail, et al. “Closed-Form Expressions for Two- and Three-Colorable States.” <i>ArXiv:2408.09515</i>, 2024.","ama":"Revis K-R, Zakaryan H, Raissi Z. Closed-Form Expressions for Two- and Three-Colorable States. <i>arXiv:240809515</i>. Published online 2024.","bibtex":"@article{Revis_Zakaryan_Raissi_2024, title={Closed-Form Expressions for Two- and Three-Colorable States}, journal={arXiv:2408.09515}, author={Revis, Konstantinos-Rafail and Zakaryan, Hrachya and Raissi, Zahra}, year={2024} }"},"publication":"arXiv:2408.09515","abstract":[{"text":"Graph states are a class of multi-partite entangled quantum states, where\r\ncolorability, a property rooted in their mathematical foundation, has\r\nsignificant implications for quantum information processing. In this study, we\r\ninvestigate the colorability of graph states in qudit systems to simplify their\r\nrepresentation and enhance their practical applications. We present closed-form\r\nexpressions for all two-colorable graph states. Our findings show that the\r\nclosed-form expression of these states is tightly linked to the graph structure\r\nand the distribution of particles in red ($n_R$) and blue ($n_B$).\r\nAdditionally, we explore a broad family of three-colorable graph states\r\nconstructed from two two-colorable graph states. The closed-form expression for\r\nthese states is in the form of one two-colorable state tensor product with the\r\ngraph basis formed from another two-colorable state. Our approach\r\nsystematically reduces the number of terms required to represent these states.\r\nFurthermore, we demonstrate that many well-known mathematical graphs, including\r\nfriendship graphs, fit within our formalism. Finally, we discuss the LU/SLOCC\r\n(Local Unitary/Stochastic Local Operation and Classical Communication)\r\nequivalence between two- and three-colorable graph states. Our findings have\r\nbroad implications for characterizing the LU/SLOCC equivalence of graph state\r\nclasses and pave the way for future research.","lang":"eng"}],"_id":"55657","language":[{"iso":"eng"}],"user_id":"98836","author":[{"first_name":"Konstantinos-Rafail","last_name":"Revis","full_name":"Revis, Konstantinos-Rafail"},{"full_name":"Zakaryan, Hrachya","first_name":"Hrachya","last_name":"Zakaryan"},{"full_name":"Raissi, Zahra","last_name":"Raissi","orcid":"0000-0002-9168-8212","first_name":"Zahra","id":"98836"}],"title":"Closed-Form Expressions for Two- and Three-Colorable States","status":"public","year":"2024","date_updated":"2024-08-20T07:19:14Z"},{"issue":"2","publication":"Physical Review Research","citation":{"ama":"Frantzeskakis R, Liu C, Raissi Z, Barnes E, Economou SE. Extracting perfect GHZ states from imperfect weighted graph states via entanglement concentration. <i>Physical Review Research</i>. 2023;5(2). doi:<a href=\"https://doi.org/10.1103/physrevresearch.5.023124\">10.1103/physrevresearch.5.023124</a>","bibtex":"@article{Frantzeskakis_Liu_Raissi_Barnes_Economou_2023, title={Extracting perfect GHZ states from imperfect weighted graph states via entanglement concentration}, volume={5}, DOI={<a href=\"https://doi.org/10.1103/physrevresearch.5.023124\">10.1103/physrevresearch.5.023124</a>}, number={2023124}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={Frantzeskakis, Rafail and Liu, Chenxu and Raissi, Zahra and Barnes, Edwin and Economou, Sophia E.}, year={2023} }","mla":"Frantzeskakis, Rafail, et al. “Extracting Perfect GHZ States from Imperfect Weighted Graph States via Entanglement Concentration.” <i>Physical Review Research</i>, vol. 5, no. 2, 023124, American Physical Society (APS), 2023, doi:<a href=\"https://doi.org/10.1103/physrevresearch.5.023124\">10.1103/physrevresearch.5.023124</a>.","short":"R. Frantzeskakis, C. Liu, Z. Raissi, E. Barnes, S.E. Economou, Physical Review Research 5 (2023).","chicago":"Frantzeskakis, Rafail, Chenxu Liu, Zahra Raissi, Edwin Barnes, and Sophia E. Economou. “Extracting Perfect GHZ States from Imperfect Weighted Graph States via Entanglement Concentration.” <i>Physical Review Research</i> 5, no. 2 (2023). <a href=\"https://doi.org/10.1103/physrevresearch.5.023124\">https://doi.org/10.1103/physrevresearch.5.023124</a>.","apa":"Frantzeskakis, R., Liu, C., Raissi, Z., Barnes, E., &#38; Economou, S. E. (2023). Extracting perfect GHZ states from imperfect weighted graph states via entanglement concentration. <i>Physical Review Research</i>, <i>5</i>(2), Article 023124. <a href=\"https://doi.org/10.1103/physrevresearch.5.023124\">https://doi.org/10.1103/physrevresearch.5.023124</a>","ieee":"R. Frantzeskakis, C. Liu, Z. Raissi, E. Barnes, and S. E. Economou, “Extracting perfect GHZ states from imperfect weighted graph states via entanglement concentration,” <i>Physical Review Research</i>, vol. 5, no. 2, Art. no. 023124, 2023, doi: <a href=\"https://doi.org/10.1103/physrevresearch.5.023124\">10.1103/physrevresearch.5.023124</a>."},"date_created":"2024-08-05T14:36:06Z","type":"journal_article","title":"Extracting perfect GHZ states from imperfect weighted graph states via entanglement concentration","year":"2023","status":"public","publication_identifier":{"issn":["2643-1564"]},"author":[{"last_name":"Frantzeskakis","first_name":"Rafail","full_name":"Frantzeskakis, Rafail"},{"last_name":"Liu","first_name":"Chenxu","full_name":"Liu, Chenxu"},{"full_name":"Raissi, Zahra","last_name":"Raissi","first_name":"Zahra","orcid":"0000-0002-9168-8212","id":"98836"},{"full_name":"Barnes, Edwin","first_name":"Edwin","last_name":"Barnes"},{"full_name":"Economou, Sophia E.","last_name":"Economou","first_name":"Sophia E."}],"publication_status":"published","date_updated":"2024-08-07T12:12:01Z","intvolume":"         5","article_number":"023124","_id":"55521","language":[{"iso":"eng"}],"publisher":"American Physical Society (APS)","user_id":"98836","doi":"10.1103/physrevresearch.5.023124","volume":5},{"has_accepted_license":"1","status":"public","ddc":["000"],"user_id":"98836","volume":106,"_id":"55522","publisher":"American Physical Society (APS)","file_date_updated":"2026-02-23T13:40:55Z","citation":{"ieee":"Z. Raissi, A. Burchardt, and E. Barnes, “General stabilizer approach for constructing highly entangled graph states,” <i>Physical Review A</i>, vol. 106, no. 6, Art. no. 062424, 2022, doi: <a href=\"https://doi.org/10.1103/physreva.106.062424\">10.1103/physreva.106.062424</a>.","mla":"Raissi, Zahra, et al. “General Stabilizer Approach for Constructing Highly Entangled Graph States.” <i>Physical Review A</i>, vol. 106, no. 6, 062424, American Physical Society (APS), 2022, doi:<a href=\"https://doi.org/10.1103/physreva.106.062424\">10.1103/physreva.106.062424</a>.","apa":"Raissi, Z., Burchardt, A., &#38; Barnes, E. (2022). General stabilizer approach for constructing highly entangled graph states. <i>Physical Review A</i>, <i>106</i>(6), Article 062424. <a href=\"https://doi.org/10.1103/physreva.106.062424\">https://doi.org/10.1103/physreva.106.062424</a>","bibtex":"@article{Raissi_Burchardt_Barnes_2022, title={General stabilizer approach for constructing highly entangled graph states}, volume={106}, DOI={<a href=\"https://doi.org/10.1103/physreva.106.062424\">10.1103/physreva.106.062424</a>}, number={6062424}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Raissi, Zahra and Burchardt, Adam and Barnes, Edwin}, year={2022} }","short":"Z. Raissi, A. Burchardt, E. Barnes, Physical Review A 106 (2022).","ama":"Raissi Z, Burchardt A, Barnes E. General stabilizer approach for constructing highly entangled graph states. <i>Physical Review A</i>. 2022;106(6). doi:<a href=\"https://doi.org/10.1103/physreva.106.062424\">10.1103/physreva.106.062424</a>","chicago":"Raissi, Zahra, Adam Burchardt, and Edwin Barnes. “General Stabilizer Approach for Constructing Highly Entangled Graph States.” <i>Physical Review A</i> 106, no. 6 (2022). <a href=\"https://doi.org/10.1103/physreva.106.062424\">https://doi.org/10.1103/physreva.106.062424</a>."},"date_updated":"2026-02-23T13:41:00Z","publication_status":"published","intvolume":"       106","year":"2022","title":"General stabilizer approach for constructing highly entangled graph states","author":[{"orcid":"0000-0002-9168-8212","last_name":"Raissi","first_name":"Zahra","full_name":"Raissi, Zahra","id":"98836"},{"full_name":"Burchardt, Adam","first_name":"Adam","last_name":"Burchardt"},{"full_name":"Barnes, Edwin","last_name":"Barnes","first_name":"Edwin"}],"publication_identifier":{"issn":["2469-9926","2469-9934"]},"doi":"10.1103/physreva.106.062424","article_number":"062424","language":[{"iso":"eng"}],"issue":"6","publication":"Physical Review A","type":"journal_article","file":[{"file_id":"64596","success":1,"content_type":"application/pdf","file_name":"PhysRevA.106.062424.pdf","file_size":483370,"access_level":"closed","relation":"main_file","date_updated":"2026-02-23T13:40:55Z","date_created":"2026-02-23T13:40:55Z","creator":"zraissi"}],"date_created":"2024-08-05T14:41:39Z"},{"publisher":"American Physical Society (APS)","_id":"55525","language":[{"iso":"eng"}],"article_number":"033411","volume":2,"user_id":"98836","doi":"10.1103/physrevresearch.2.033411","author":[{"id":"98836","full_name":"Raissi, Zahra","orcid":"0000-0002-9168-8212","last_name":"Raissi","first_name":"Zahra"},{"full_name":"Teixidó, Adam","last_name":"Teixidó","first_name":"Adam"},{"full_name":"Gogolin, Christian","last_name":"Gogolin","first_name":"Christian"},{"first_name":"Antonio","last_name":"Acín","full_name":"Acín, Antonio"}],"publication_identifier":{"issn":["2643-1564"]},"status":"public","title":"Constructions of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>-uniform and absolutely maximally entangled states beyond maximum distance codes","year":"2020","intvolume":"         2","publication_status":"published","date_updated":"2024-08-07T12:12:40Z","date_created":"2024-08-05T14:44:05Z","type":"journal_article","citation":{"bibtex":"@article{Raissi_Teixidó_Gogolin_Acín_2020, title={Constructions of &#60;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&#62;&#60;mml:mi&#62;k&#60;/mml:mi&#62;&#60;/mml:math&#62;-uniform and absolutely maximally entangled states beyond maximum distance codes}, volume={2}, DOI={<a href=\"https://doi.org/10.1103/physrevresearch.2.033411\">10.1103/physrevresearch.2.033411</a>}, number={3033411}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={Raissi, Zahra and Teixidó, Adam and Gogolin, Christian and Acín, Antonio}, year={2020} }","ama":"Raissi Z, Teixidó A, Gogolin C, Acín A. Constructions of &#60;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&#62;&#60;mml:mi&#62;k&#60;/mml:mi&#62;&#60;/mml:math&#62;-uniform and absolutely maximally entangled states beyond maximum distance codes. <i>Physical Review Research</i>. 2020;2(3). doi:<a href=\"https://doi.org/10.1103/physrevresearch.2.033411\">10.1103/physrevresearch.2.033411</a>","mla":"Raissi, Zahra, et al. “Constructions of &#60;mml:Math Xmlns:Mml=\"http://Www.W3.Org/1998/Math/MathML\"&#62;&#60;mml:Mi&#62;k&#60;/Mml:Mi&#62;&#60;/Mml:Math&#62;-Uniform and Absolutely Maximally Entangled States beyond Maximum Distance Codes.” <i>Physical Review Research</i>, vol. 2, no. 3, 033411, American Physical Society (APS), 2020, doi:<a href=\"https://doi.org/10.1103/physrevresearch.2.033411\">10.1103/physrevresearch.2.033411</a>.","short":"Z. Raissi, A. Teixidó, C. Gogolin, A. Acín, Physical Review Research 2 (2020).","chicago":"Raissi, Zahra, Adam Teixidó, Christian Gogolin, and Antonio Acín. “Constructions of &#60;mml:Math Xmlns:Mml=\"http://Www.W3.Org/1998/Math/MathML\"&#62;&#60;mml:Mi&#62;k&#60;/Mml:Mi&#62;&#60;/Mml:Math&#62;-Uniform and Absolutely Maximally Entangled States beyond Maximum Distance Codes.” <i>Physical Review Research</i> 2, no. 3 (2020). <a href=\"https://doi.org/10.1103/physrevresearch.2.033411\">https://doi.org/10.1103/physrevresearch.2.033411</a>.","ieee":"Z. Raissi, A. Teixidó, C. Gogolin, and A. Acín, “Constructions of &#60;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&#62;&#60;mml:mi&#62;k&#60;/mml:mi&#62;&#60;/mml:math&#62;-uniform and absolutely maximally entangled states beyond maximum distance codes,” <i>Physical Review Research</i>, vol. 2, no. 3, Art. no. 033411, 2020, doi: <a href=\"https://doi.org/10.1103/physrevresearch.2.033411\">10.1103/physrevresearch.2.033411</a>.","apa":"Raissi, Z., Teixidó, A., Gogolin, C., &#38; Acín, A. (2020). Constructions of &#60;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&#62;&#60;mml:mi&#62;k&#60;/mml:mi&#62;&#60;/mml:math&#62;-uniform and absolutely maximally entangled states beyond maximum distance codes. <i>Physical Review Research</i>, <i>2</i>(3), Article 033411. <a href=\"https://doi.org/10.1103/physrevresearch.2.033411\">https://doi.org/10.1103/physrevresearch.2.033411</a>"},"publication":"Physical Review Research","issue":"3"},{"file_date_updated":"2026-02-23T13:42:24Z","citation":{"bibtex":"@article{Burchardt_Raissi_2020, title={Stochastic local operations with classical communication of absolutely maximally entangled states}, volume={102}, DOI={<a href=\"https://doi.org/10.1103/physreva.102.022413\">10.1103/physreva.102.022413</a>}, number={2022413}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Burchardt, Adam and Raissi, Zahra}, year={2020} }","chicago":"Burchardt, Adam, and Zahra Raissi. “Stochastic Local Operations with Classical Communication of Absolutely Maximally Entangled States.” <i>Physical Review A</i> 102, no. 2 (2020). <a href=\"https://doi.org/10.1103/physreva.102.022413\">https://doi.org/10.1103/physreva.102.022413</a>.","short":"A. Burchardt, Z. Raissi, Physical Review A 102 (2020).","ama":"Burchardt A, Raissi Z. Stochastic local operations with classical communication of absolutely maximally entangled states. <i>Physical Review A</i>. 2020;102(2). doi:<a href=\"https://doi.org/10.1103/physreva.102.022413\">10.1103/physreva.102.022413</a>","ieee":"A. Burchardt and Z. Raissi, “Stochastic local operations with classical communication of absolutely maximally entangled states,” <i>Physical Review A</i>, vol. 102, no. 2, Art. no. 022413, 2020, doi: <a href=\"https://doi.org/10.1103/physreva.102.022413\">10.1103/physreva.102.022413</a>.","mla":"Burchardt, Adam, and Zahra Raissi. “Stochastic Local Operations with Classical Communication of Absolutely Maximally Entangled States.” <i>Physical Review A</i>, vol. 102, no. 2, 022413, American Physical Society (APS), 2020, doi:<a href=\"https://doi.org/10.1103/physreva.102.022413\">10.1103/physreva.102.022413</a>.","apa":"Burchardt, A., &#38; Raissi, Z. (2020). Stochastic local operations with classical communication of absolutely maximally entangled states. <i>Physical Review A</i>, <i>102</i>(2), Article 022413. <a href=\"https://doi.org/10.1103/physreva.102.022413\">https://doi.org/10.1103/physreva.102.022413</a>"},"has_accepted_license":"1","status":"public","user_id":"98836","ddc":["000"],"volume":102,"_id":"55524","publisher":"American Physical Society (APS)","publication":"Physical Review A","issue":"2","type":"journal_article","file":[{"file_id":"64598","content_type":"application/pdf","success":1,"relation":"main_file","date_updated":"2026-02-23T13:42:24Z","file_name":"PhysRevA.102.022413.pdf","file_size":836678,"access_level":"closed","date_created":"2026-02-23T13:42:24Z","creator":"zraissi"}],"date_created":"2024-08-05T14:43:35Z","publication_status":"published","date_updated":"2026-02-23T13:44:06Z","intvolume":"       102","year":"2020","title":"Stochastic local operations with classical communication of absolutely maximally entangled states","publication_identifier":{"issn":["2469-9926","2469-9934"]},"author":[{"full_name":"Burchardt, Adam","first_name":"Adam","last_name":"Burchardt"},{"first_name":"Zahra","orcid":"0000-0002-9168-8212","last_name":"Raissi","full_name":"Raissi, Zahra","id":"98836"}],"doi":"10.1103/physreva.102.022413","article_number":"022413","language":[{"iso":"eng"}]},{"citation":{"ieee":"Z. Raissi, “Modifying Method of Constructing Quantum Codes From Highly Entangled States,” <i>IEEE Access</i>, vol. 8, pp. 222439–222448, 2020, doi: <a href=\"https://doi.org/10.1109/access.2020.3043401\">10.1109/access.2020.3043401</a>.","mla":"Raissi, Zahra. “Modifying Method of Constructing Quantum Codes From Highly Entangled States.” <i>IEEE Access</i>, vol. 8, Institute of Electrical and Electronics Engineers (IEEE), 2020, pp. 222439–48, doi:<a href=\"https://doi.org/10.1109/access.2020.3043401\">10.1109/access.2020.3043401</a>.","apa":"Raissi, Z. (2020). Modifying Method of Constructing Quantum Codes From Highly Entangled States. <i>IEEE Access</i>, <i>8</i>, 222439–222448. <a href=\"https://doi.org/10.1109/access.2020.3043401\">https://doi.org/10.1109/access.2020.3043401</a>","bibtex":"@article{Raissi_2020, title={Modifying Method of Constructing Quantum Codes From Highly Entangled States}, volume={8}, DOI={<a href=\"https://doi.org/10.1109/access.2020.3043401\">10.1109/access.2020.3043401</a>}, journal={IEEE Access}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Raissi, Zahra}, year={2020}, pages={222439–222448} }","ama":"Raissi Z. Modifying Method of Constructing Quantum Codes From Highly Entangled States. <i>IEEE Access</i>. 2020;8:222439-222448. doi:<a href=\"https://doi.org/10.1109/access.2020.3043401\">10.1109/access.2020.3043401</a>","short":"Z. 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