{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T14:30:37Z","timestamp":1775313037611,"version":"3.50.1"},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2007,12,1]],"date-time":"2007-12-01T00:00:00Z","timestamp":1196467200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2007,12]]},"abstract":"<jats:p>We give an algorithm allowing the construction of bases of local unitary invariants of pure <jats:italic>k<\/jats:italic>-qubit states from a knowledge of the polynomial covariants of the group of invertible local filtering operations. The simplest invariants obtained in this way are made explicit and compared with various known entanglement measures. Complete sets of generators are obtained for up to four qubits, and the structure of the invariant algebras is discussed in detail.<\/jats:p>","DOI":"10.1017\/s0960129507006330","type":"journal-article","created":{"date-parts":[[2007,11,23]],"date-time":"2007-11-23T13:42:02Z","timestamp":1195825322000},"page":"1133-1151","source":"Crossref","is-referenced-by-count":16,"title":["Unitary invariants of qubit systems"],"prefix":"10.1017","volume":"17","author":[{"given":"JEAN-GABRIEL","family":"LUQUE","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JEAN-YVES","family":"THIBON","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FR\u00c9D\u00c9RIC","family":"TOUMAZET","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2007,12,1]]},"reference":[{"key":"S0960129507006330_manual_ref-28","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(96)00803-1"},{"key":"S0960129507006330_manual_ref-24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.67.012108"},{"key":"S0960129507006330_manual_ref-21","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/2\/007"},{"key":"S0960129507006330_manual_ref-12","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/37\/34\/008"},{"key":"S0960129507006330_manual_ref-30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.65.052112"},{"key":"S0960129507006330_manual_ref-10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.62.062314"},{"key":"S0960129507006330_manual_ref-23","doi-asserted-by":"publisher","DOI":"10.1063\/1.1497700"},{"key":"S0960129507006330_manual_ref-1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.49.91"},{"key":"S0960129507006330_manual_ref-11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.47.777"},{"key":"S0960129507006330_manual_ref-5","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/36\/38\/309"},{"key":"S0960129507006330_manual_ref-3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.69.2881"},{"key":"S0960129507006330_manual_ref-17","unstructured":"Klyachko, A. A. (2002) Coherent states, entanglement, and geometric invariant theory, quant-ph\/0206012"},{"key":"S0960129507006330_manual_ref-15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.58.1833"},{"key":"S0960129507006330_manual_ref-18","doi-asserted-by":"publisher","DOI":"10.1088\/1464-4266\/5\/3\/364"},{"key":"S0960129507006330_manual_ref-7","doi-asserted-by":"crossref","unstructured":"Brylinski, J.-L. (2002) Algebraic measures of entanglement. In: Brylinski, R. K. and Chen, G. (eds.) Mathematics of quantum computation, Computational Mathematics Series 3, Chapman and Hall\/CRC 3\u201323.","DOI":"10.1201\/9781420035377.pt1"},{"key":"S0960129507006330_manual_ref-14","unstructured":"Grassl, M. (2002) Entanglement and invariant theory. Transparencies of a talk reporting on joint work with T. Beth, M. R\u00f6tteler and Yu. Makhlin. (Available at http:\/\/iaks-www.ira.uka.de\/home\/grassl\/paper\/MSRI_InvarTheory.pdf.)"},{"key":"S0960129507006330_manual_ref-27","doi-asserted-by":"publisher","DOI":"10.1142\/S0219749906001980"},{"key":"S0960129507006330_manual_ref-9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.23.880"},{"key":"S0960129507006330_manual_ref-8","doi-asserted-by":"crossref","unstructured":"Brylinski, J.-L. and Brylinski, R. (2002) Invariant polynomial functions on k qudits. In: Brylinski, R. K. and Chen, G. (eds.) Mathematics of quantum computation, Computational Mathematics Series 3, Chapman and Hall\/CRC 277\u2013286.","DOI":"10.1201\/9781420035377.pt6"},{"key":"S0960129507006330_manual_ref-26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.72.012337"},{"key":"S0960129507006330_manual_ref-22","volume-title":"Symmetric functions and Hall polynomials","author":"Macdonald","year":"1991"},{"key":"S0960129507006330_manual_ref-29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.52.4396"},{"key":"S0960129507006330_manual_ref-31","doi-asserted-by":"publisher","DOI":"10.37236\/1811"},{"key":"S0960129507006330_manual_ref-20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.67.042303"},{"key":"S0960129507006330_manual_ref-25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623660"},{"key":"S0960129507006330_manual_ref-13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.37.465"},{"key":"S0960129507006330_manual_ref-4","first-page":"619","article-title":"An observable measure of entanglement for pure states of multi-qubit systems","volume":"3","author":"Brennen","year":"2003","journal-title":"Quantum. Inf. Comput."},{"key":"S0960129507006330_manual_ref-6","doi-asserted-by":"publisher","DOI":"10.1063\/1.1809255"},{"key":"S0960129507006330_manual_ref-2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.38.447"},{"key":"S0960129507006330_manual_ref-16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.60.910"},{"key":"S0960129507006330_manual_ref-19","first-page":"1103","article-title":"Sur les formes trilin\u00e9aires","volume":"92","author":"Le Paige","year":"1881","journal-title":"C. R. Acad. Sci. Paris"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129507006330","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T06:00:33Z","timestamp":1750485633000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129507006330\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12]]},"references-count":31,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2007,6]]}},"alternative-id":["S0960129507006330"],"URL":"https:\/\/doi.org\/10.1017\/s0960129507006330","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12]]}}}