Symmetric multiqudit states: Stars, entanglement, and rotosensors

Complex weights; Majorana; Multipartite entanglements; Multipartite state; Pure state; Quantum state; Spin state; Symmetric state; Atomic and Molecular Physics, and Optics; Quantum Physics; Mathematical Physics

Abstract :

[en] A constellation of N=d-1 Majorana stars represents an arbitrary pure quantum state of dimension d or a permutation-symmetric state of a system consisting of n qubits. We generalize the latter construction to represent in a similar way an arbitrary symmetric pure state of k subsystems with d levels each. For d≥3, such states are equivalent, as far as rotations are concerned, to a collection of various spin states, with definite relative complex weights. Following Majorana's lead, we introduce a multiconstellation, consisting of the Majorana constellations of the above spin states, augmented by an auxiliary, "spectator"constellation, encoding the complex weights. Examples of stellar representations of symmetric states of four qutrits, and two spin-3/2 systems, are presented. We revisit the Hermite and Murnaghan isomorphisms, which relate multipartite states of various spins, number of parties, and even symmetries. We show how the tools introduced can be used to analyze multipartite entanglement and to identify optimal quantum rotosensors, i.e., pure states which are maximally sensitive to rotations around a specified axis, or averaged over all axes.

Disciplines :

Physics

Author, co-author :

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

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

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

Braun, Daniel ; Institut für Theoretische Physik, Universität Tübingen, Tübingen, Germany

Serrano Ensástiga, Eduardo ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM) ; Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México, Ensenada, Mexico

Zyczkowski, Karol ; Institute of Theoretical Physics, Jagiellonian University, Kraków, Poland ; Center for Theoretical Physics, Polish Academy of Sciences, Warsaw, Poland

Language :

English

Title :

Symmetric multiqudit states: Stars, entanglement, and rotosensors

Publication date :

July 2021

Journal title :

Physical Review. A

ISSN :

2469-9926

eISSN :

2469-9934

Publisher :

American Physical Society

Volume :

104

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.aps.org/article/10.1103/PhysRevA.104.012407

Funders :

UNAM - Universidad Nacional Autónoma de México
CONACYT - Consejo Nacional de Ciencia y Tecnología
NCN - Narodowe Centrum Nauki

Funding text :

C.C., L.H., and E.S.-E. would like to acknowledge partial financial support from the DGAPA PAPIIT project IN111920 of UNAM. E.S.-E. would also like to acknowledge support from a postdoctoral fellowship of CONACYT (Mexico). Financial support by the Polish National Science Center under the Grant No. DEC-2015/18/A/ST2/00274 and by Foundation for Polish Science under the Team-Net NTQC project is gratefully acknowledged.

Available on ORBi :

since 22 December 2025

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