{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:52:23Z","timestamp":1760057543148,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T00:00:00Z","timestamp":1739491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CONAHCyT scholarship","award":["CIIC 2024-proyecto 043\/2024"],"award-info":[{"award-number":["CIIC 2024-proyecto 043\/2024"]}]},{"name":"Universidad de Guanajuato","award":["CIIC 2024-proyecto 043\/2024"],"award-info":[{"award-number":["CIIC 2024-proyecto 043\/2024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The understanding of the properties of multipartite systems is a long-standing challenge in quantum theory that signals the need for new ideas and alternative frameworks that can shed light on the intricacies of quantum behavior. In this work, we argue that symmetric spaces provide a common language to describe two-qubit and two-mode Gaussian systems. Our approach relies on the use of equivalence classes that are defined by a subgroup of the maximal symmetry group of the system and involves an involution which enables the Cartan decomposition of the group elements. We work out the symmetric spaces of two qubits and two modes to identify classes which include an equal degree of mixing states, product states, and X states, among others. For three qubits and three modes, we point out how the framework can be generalized and report partial results about the physical interpretations of the symmetric spaces.<\/jats:p>","DOI":"10.3390\/sym17020292","type":"journal-article","created":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T06:52:01Z","timestamp":1739515921000},"page":"292","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetric Spaces of Qubits and Gaussian Modes"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-4054-1595","authenticated-orcid":false,"given":"Antonio de Jes\u00fas Castillo","family":"Moctezuma","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidad de Guanajuato, Loma del Bosque 135, Le\u00f3n Guanajuato 37150, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2531-0772","authenticated-orcid":false,"given":"Jos\u00e9 Luis","family":"Lucio","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad de Guanajuato, Loma del Bosque 135, Le\u00f3n Guanajuato 37150, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-5155-2554","authenticated-orcid":false,"given":"Alan Josu\u00e9","family":"Sierra-Torres","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad de Guanajuato, Loma del Bosque 135, Le\u00f3n Guanajuato 37150, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1016\/0315-0860(84)90028-4","article-title":"The Erlanger Programm of Felix Klein: Reflections on its place in the history of mathematics","volume":"11","author":"Hawkins","year":"1984","journal-title":"Hist. 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