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@ARTICLE{Sauer:904591,
      author       = {Sauer, A and Bernád, J. Z. and Moreno, H. J. and Alber,
                      G.},
      title        = {{E}ntanglement in bipartite quantum systems: {E}uclidean
                      volume ratios and detectability by {B}ell inequalities},
      journal      = {Journal of physics / A},
      volume       = {54},
      number       = {49},
      issn         = {0022-3689},
      address      = {Bristol},
      publisher    = {IOP Publ.},
      reportid     = {FZJ-2021-06161},
      pages        = {495302 -},
      year         = {2021},
      abstract     = {Euclidean volume ratios between quantum states with
                      positive partial transpose and all quantum states in
                      bipartite systems are investigated. These ratios allow a
                      quantitative exploration of the typicality of entanglement
                      and of its detectability by Bell inequalities. For this
                      purpose a new numerical approach is developed. It is based
                      on the Peres–Horodecki criterion, on a characterization of
                      the convex set of quantum states by inequalities resulting
                      from Newton identities and from Descartes' rule of signs,
                      and on a numerical approach involving the multiphase Monte
                      Carlo method and the hit-and-run algorithm. This approach
                      confirms not only recent analytical and numerical results on
                      two-qubit, qubit-qutrit, and qubit-four-level qudit states
                      but also allows for a numerically reliable numerical
                      treatment of so far unexplored qutrit–qutrit states. Based
                      on this numerical approach with the help of the
                      Clauser–Horne–Shimony–Holt inequality and the
                      Collins–Gisin inequality the degree of detectability of
                      entanglement is investigated for two-qubit quantum states.
                      It is investigated quantitatively to which extent a combined
                      test of both Bell inequalities can increase the
                      detectability of entanglement beyond what is achievable by
                      each of these inequalities separately.},
      cin          = {PGI-8},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-8-20190808},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5221},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000720541800001},
      doi          = {10.1088/1751-8121/ac3469},
      url          = {https://juser.fz-juelich.de/record/904591},
}