{"title":"Closed-Form Expressions for Two- and Three-Colorable States","citation":{"ama":"Revis K-R, Zakaryan H, Raissi Z. Closed-Form Expressions for Two- and Three-Colorable States. <i>arXiv:240809515</i>. Published online 2024.","short":"K.-R. Revis, H. Zakaryan, Z. Raissi, ArXiv:2408.09515 (2024).","ieee":"K.-R. Revis, H. Zakaryan, and Z. Raissi, “Closed-Form Expressions for Two- and Three-Colorable States,” <i>arXiv:2408.09515</i>. 2024.","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>.","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} }","mla":"Revis, Konstantinos-Rafail, et al. “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."},"user_id":"98836","publication":"arXiv:2408.09515","date_created":"2024-08-20T07:18:02Z","external_id":{"arxiv":["2408.09515"]},"_id":"55657","type":"preprint","abstract":[{"lang":"eng","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."}],"status":"public","year":"2024","language":[{"iso":"eng"}],"date_updated":"2024-08-20T07:19:14Z","author":[{"last_name":"Revis","first_name":"Konstantinos-Rafail","full_name":"Revis, Konstantinos-Rafail"},{"full_name":"Zakaryan, Hrachya","last_name":"Zakaryan","first_name":"Hrachya"},{"last_name":"Raissi","id":"98836","first_name":"Zahra","full_name":"Raissi, Zahra","orcid":"0000-0002-9168-8212"}]}