Majorana representation for mixed states

Density matrix; Hermitian operators; Homogeneous polynomials; Majorana representation; Original state; Projective spaces; Spin densities; Tensor representation; Atomic and Molecular Physics, and Optics; Quantum Physics

Abstract :

[en] We generalize the Majorana stellar representation of spin-s pure states to mixed states, and in general to any Hermitian operator, defining a bijective correspondence between three spaces: The spin-density matrices, a projective space of homogeneous polynomials of four variables, and a set of equivalence classes of points (constellations) on spheres of different radii. The representation behaves well under rotations by construction, and also under partial traces where the reduced density matrices inherit their constellation classes from the original state ρ. We express several concepts and operations related to density matrices in terms of the corresponding polynomials, such as the anticoherence criterion and the tensor representation of spin-s states described in Giraud et al. [Phys. Rev. Lett. 114, 080401 (2015)].PRLTAO0031-900710.1103/PhysRevLett.114.080401

Disciplines :

Physics

Author, co-author :

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

Braun, D. ; Institut für Theoretische Physik, Universität Tübingen, Tübingen, Germany

Language :

English

Title :

Majorana representation for mixed states

Publication date :

February 2020

Journal title :

Physical Review. A

ISSN :

2469-9926

eISSN :

2469-9934

Publisher :

American Physical Society

Volume :

101

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.aps.org/article/10.1103/PhysRevA.101.022332

Funding text :

E.S.-E. thanks the University Tübingen and its T@T fellowship. The authors thank John Martin for fruitful correspondence.

Available on ORBi :

since 22 December 2025

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