% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@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},
}