{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T21:45:31Z","timestamp":1773265531384,"version":"3.50.1"},"reference-count":40,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2019,1,6]],"date-time":"2019-01-06T00:00:00Z","timestamp":1546732800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"For a multipart quantum system, a locally maximally entangled (LME) state is one where each elementary subsystem is maximally entangled with its complement. This paper is a sequel to~[J. Bryan, Z. Reichstein and M. Van Raamsdonk, Existence of Locally Maximally Entangled Quantum States via Geometric Invariant Theory, Ann. Henri Poincar\u00e9 19 (2018), no. 8, 2491-2511. MR3830220], which gives necessary and sufficient conditions for a system to admit LME states in terms of its subsystem dimensions(<\/mml:mo>d<\/mml:mi>1<\/mml:mn><\/mml:msub>,<\/mml:mo>d<\/mml:mi>2<\/mml:mn><\/mml:msub>,<\/mml:mo>\u2026<\/mml:mo>,<\/mml:mo>d<\/mml:mi>n<\/mml:mi><\/mml:msub>)<\/mml:mo><\/mml:math>, and computes the dimension of the spaceS<\/mml:mi><\/mml:mrow>L<\/mml:mi>M<\/mml:mi>E<\/mml:mi><\/mml:mrow><\/mml:msub>\/<\/mml:mo><\/mml:mrow>K<\/mml:mi><\/mml:math>of LME states up to local unitary transformations for all non-empty cases. Here we provide a pedagogical overview and physical interpretation of the underlying mathematics that leads to these results and give a large class of explicit constructions for LME states. In particular, we construct all LME states for tripartite systems with subsystem dimensions(<\/mml:mo>2<\/mml:mn>,<\/mml:mo>A<\/mml:mi>,<\/mml:mo>B<\/mml:mi>)<\/mml:mo><\/mml:math>and give a general representation-theoretic construction for a special class of stabilizer LME states. The latter construction provides a common framework for many known LME states. Our results have direct implications for the problem of characterizing SLOCC equivalence classes of quantum states, since points inS<\/mml:mi><\/mml:mrow>L<\/mml:mi>M<\/mml:mi>E<\/mml:mi><\/mml:mrow><\/mml:msub>\/<\/mml:mo><\/mml:mrow>K<\/mml:mi><\/mml:math>correspond to natural families of SLOCC classes. Finally, we give the dimension of the stabilizer subgroupS<\/mml:mi>\u2282<\/mml:mo>SL<\/mml:mi>\u2061<\/mml:mo>(<\/mml:mo>d<\/mml:mi>1<\/mml:mn><\/mml:msub>,<\/mml:mo>C<\/mml:mi><\/mml:mrow>)<\/mml:mo>\u00d7<\/mml:mo>\u22ef<\/mml:mo>\u00d7<\/mml:mo>SL<\/mml:mi>\u2061<\/mml:mo>(<\/mml:mo>d<\/mml:mi>n<\/mml:mi><\/mml:msub>,<\/mml:mo>C<\/mml:mi><\/mml:mrow>)<\/mml:mo><\/mml:math>for a generic state in an arbitrary multipart system and identify all cases where this stabilizer is trivial.<\/jats:p>","DOI":"10.22331\/q-2019-01-06-115","type":"journal-article","created":{"date-parts":[[2019,1,6]],"date-time":"2019-01-06T14:12:54Z","timestamp":1546783974000},"page":"115","source":"Crossref","is-referenced-by-count":13,"title":["Locally Maximally Entangled States of Multipart Quantum Systems"],"prefix":"10.22331","volume":"3","author":[{"given":"Jim","family":"Bryan","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., V6T 1Z1, Canada"}]},{"given":"Samuel","family":"Leutheusser","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, B.C., V6T 1Z2, Canada"},{"name":"Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA"}]},{"given":"Zinovy","family":"Reichstein","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., V6T 1Z1, Canada"}]},{"given":"Mark Van","family":"Raamsdonk","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, B.C., V6T 1Z2, Canada"}]}],"member":"9598","published-online":{"date-parts":[[2019,1,6]]},"reference":[{"key":"0","doi-asserted-by":"crossref","unstructured":"I. 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