{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T13:50:08Z","timestamp":1779112208567,"version":"3.51.4"},"reference-count":26,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2003,10]]},"abstract":"<jats:p> Given a pure state |\u03c8<jats:sub>N<\/jats:sub>&gt;\u2208\u210b<jats:sub>N<\/jats:sub> of a quantum system composed of n qubits, where \u210b<jats:sub>N<\/jats:sub> is the Hilbert space of dimension N=2<jats:sup>n<\/jats:sup>, this paper answers two questions: what conditions should the amplitudes in |\u03c8<jats:sub>N<\/jats:sub>&gt; satisfy for this state to be separable (i) into a tensor product of n qubit states |\u03c8<jats:sub>2<\/jats:sub>&gt;<jats:sub>0<\/jats:sub>\u2297 |\u03c8<jats:sub>2<\/jats:sub>&gt;<jats:sub>1<\/jats:sub> \u2297\u22ef\u2297 |\u03c8<jats:sub>2<\/jats:sub>&gt;<jats:sub>n-1<\/jats:sub>, and (ii), into a tensor product of two subsystems states |\u03c8<jats:sub>P<\/jats:sub>&gt; \u2297 |\u03c8<jats:sub>Q<\/jats:sub>&gt; with P=2<jats:sup>p<\/jats:sup> and Q=2<jats:sup>q<\/jats:sup> such that p+q=n? For both questions, necessary and sufficient conditions are proved, thus characterizing at the same time families of separable and entangled states of n qubit systems. A number of more refined questions about separability in n qubit systems can be studied on the basis of these results. <\/jats:p>","DOI":"10.1142\/s0129054103002035","type":"journal-article","created":{"date-parts":[[2003,11,24]],"date-time":"2003-11-24T09:26:19Z","timestamp":1069665979000},"page":"797-814","source":"Crossref","is-referenced-by-count":7,"title":["SEPARABILITY OF PURE N-QUBIT STATES: TWO CHARACTERIZATIONS"],"prefix":"10.1142","volume":"14","author":[{"given":"PHILIPPE","family":"JORRAND","sequence":"first","affiliation":[{"name":"Leibniz Laboratory, 46 av F\u00e9lix-Viallet, Grenoble, 38000, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MEHDI","family":"MHALLA","sequence":"additional","affiliation":[{"name":"Leibniz Laboratory, 46 av F\u00e9lix-Viallet, Grenoble, 38000, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.87.040401"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.70.1895"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.69.2881"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1063\/1.1494474"},{"key":"rf7","volume":"49","author":"Bru\u00df D.","journal-title":"Journal of Modern Optics"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539797324886"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(02)01538-4"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.56.1201"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.88.187904"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.83.3562"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.62.062314"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.67.661"},{"key":"rf18","volume-title":"Quantum computing","author":"Gruska J.","year":"1999"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(96)00706-2"},{"key":"rf21","volume":"283","author":"Horodecki M.","journal-title":"Physics Letters A"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(97)00416-7"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.62.032310"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.61.062302"},{"key":"rf32","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.89.207901"},{"key":"rf33","volume-title":"Quantum computation and quantum information","author":"Nielsen M. A.","year":"2000"},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.77.1413"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.65.032328"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/33\/21\/308"},{"key":"rf39","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539795293172"},{"key":"rf40","volume":"65","author":"Verstraete F.","journal-title":"Physical Review A"},{"key":"rf42","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.40.4277"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054103002035","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:37:50Z","timestamp":1565138270000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054103002035"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,10]]},"references-count":26,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,10]]}},"alternative-id":["10.1142\/S0129054103002035"],"URL":"https:\/\/doi.org\/10.1142\/s0129054103002035","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,10]]}}}