Stellar Representation of Multipartite Antisymmetric States

[en] Pure quantum spin-s states can be represented by 2s points on the sphere, as shown by Majorana (Nuovo Cimento 9:43–50, 1932)—the description has proven particularly useful in the study of rotational symmetries of the states, and a host of other properties, as the points rotate rigidly on the sphere when the state undergoes an SU(2) transformation in Hilbert space. We present here an extension of this representation to multipartite, totally antisymmetric (under exchange of any two qudits) states, widely known in the form of Slater determinants, and linear combinations thereof. Such states generally involve a superposition of various spin values, giving rise to a family of Majorana-like constellations, that captures their rotational transformation properties. We also point out that our results apply equally well to the characterization of degenerate linear subspaces of the Hilbert space of a single spin, of the type that appear in the Wilczek–Zee effect, and comment on potential applications to holonomic quantum computing.

Disciplines :

Physics

Author, co-author :

Chryssomalakos, C. ; Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, CDMX, Mexico

Guzmán-González, E. ; Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, CDMX, Mexico

Hanotel, L. ; Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, CDMX, Mexico

Serrano Ensástiga, Eduardo ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM) ; Institut für Theoretische Physik, Universität Tübingen, Tübingen, Germany

Language :

English

Title :

Stellar Representation of Multipartite Antisymmetric States

Publication date :

2021

Journal title :

Communications in Mathematical Physics

ISSN :

0010-3616

eISSN :

1432-0916

Publisher :

Springer Science and Business Media Deutschland GmbH

Volume :

381

Issue :

Pages :

735 - 764

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.springer.com/content/pdf/10.1007/s00220-020-03918-7.pdf

Funders :

University of Tübingen
UNAM - National Autonomous University of Mexico

Funding text :

The authors would like to acknowledge partial financial support from UNAM-DGAPA-PAPIIT projects IG100316 and IN111920. ESE would also like to acknowledge financial support from the T@T fellowship of the University of Tübingen.

Available on ORBi :

since 22 December 2025

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