Spin-Coupling Diagrams and Incidence Geometry: A Note on Combinatorial and Quantum-Computational Aspects

  • Manuela S. Arruda
  • Robenilson F. Santos
  • Dimitri Marinelli
  • Vincenzo Aquilanti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9786)


This paper continues previous work on quantum mechanical angular momentum theory and its applications. Relationships with projective geometry provide insight on various areas of physics and computational science. The seven-spin network previously introduced and the associate diagrams are contrasted to those of the Fano plane and its intriguing missing triad is discussed graphically. The two graphs are suggested as combinatorial and finite-geometrical “abacus” for quantum information applications, specifically for either (i)- a fermion-boson protocol, the hardware being typically a magnetic moiety distinguishing odd and even spins, or (ii)- a quantum-classical protocol, the hardware being materials (arguably molecular radicals) with both large and small angular momentum states.


Angular-momentum Spin-coupling Projective-geometry 



Manuela Arruda is grateful to Brazilian CNPq for a post doctoral fellowship to the Perugia University. Vincenzo Aquilanti thanks Brazilian Capes for a Special Visiting Professorship at the Bahia Federal University, and Roger Anderson (Santa Cruz, California), Ana Carla Bitencourt and Mirco Ragni (Feira de Santana, Bahia, Brazil), Robert Littlejohn (Berkeley, California), Cecilia Coletti (Chieti, Italy), Annalisa Marzuoli (Pavia, Italy) and Frederico Prudente (Salvador, Bahia, Brazil) for inspiring and productive collaborations over the years. Vincenzo Aquilanti is grateful to the support of the Italian MIUR through the SIR 2014 Grant RBSI14U3VF.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Manuela S. Arruda
    • 1
    • 4
  • Robenilson F. Santos
    • 2
    • 3
  • Dimitri Marinelli
    • 4
  • Vincenzo Aquilanti
    • 4
  1. 1.Centro de Ciências Exatas e TecnológicasUniversidade Federal do Recôncavo da BahiaCruz das AlmasBrazil
  2. 2.Instituto de FísicaUniversidade Federal da BahiaSalvadorBrazil
  3. 3.Instituto Federal de Alagoas, Campus PiranhasPiranhasBrazil
  4. 4.Dipartmento di Chimica, Biologia and BiotecnologieUniversità di PerugiaPerugiaItaly

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