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@ARTICLE{Leiner:875409,
author = {Leiner, David and Zeier, Robert and Glaser, Steffen J.},
title = {{S}ymmetry-adapted decomposition of tensor operators and
the visualization of coupled spin systems},
journal = {Journal of physics / A Mathematical and theoretical},
volume = {53},
number = {49},
issn = {0022-3689},
address = {Bristol},
publisher = {IOP Publ.},
reportid = {FZJ-2020-02018},
pages = {495301},
year = {2020},
abstract = {We study the representation and visualization of
finite-dimensional, coupled quantum systems. To establish a
generalized Wigner representation, multi-spin operators are
decomposed into a symmetry-adapted tensor basis and are
mapped to multiple spherical plots that are each assembled
from linear combinations of spherical harmonics. We
explicitly determine the corresponding symmetry-adapted
tensor basis for up to six coupled spins 1/2 (qubits) using
a first step that relies on a Clebsch-Gordan decomposition
and a second step which is implemented with two different
approaches based on explicit projection operators and
coefficients of fractional parentage. The approach based on
explicit projection operator is currently only applicable
for up to four spins 1/2. The resulting generalized Wigner
representation is illustrated with various examples for the
cases of four to six coupled spins 1/2. We also treat the
case of two coupled spins with arbitrary spin numbers
(qudits) not necessarily equal to 1/2 and highlight a
quantum system of a spin 1/2 coupled to a spin 1 (qutrit).
Our work offers a much more detailed understanding of the
symmetries appearing in coupled quantum systems.},
cin = {PGI-8},
ddc = {530},
cid = {I:(DE-Juel1)PGI-8-20190808},
pnm = {142 - Controlling Spin-Based Phenomena (POF3-142) / 522 -
Controlling Spin-Based Phenomena (POF3-522) / PASQuanS -
Programmable Atomic Large-Scale Quantum Simulation (817482)},
pid = {G:(DE-HGF)POF3-142 / G:(DE-HGF)POF3-522 /
G:(EU-Grant)817482},
typ = {PUB:(DE-HGF)16},
UT = {WOS:000615524500001},
doi = {10.1088/1751-8121/ab93ff},
url = {https://juser.fz-juelich.de/record/875409},
}