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Pentagrams and Paradoxes

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Abstract

Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and then show how the pentagram underlies a number of other quantum “paradoxes”, such as that of Hardy.

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Authors and Affiliations

  1. AlbaNova, Fysikum, Stockholms Universitet, 106 91, Stockholm, Sweden

    Piotr Badzia̧g & Ingemar Bengtsson

  2. Dep. Física Aplicada II, Universidad de Sevilla, 410 12, Sevilla, Spain

    Adán Cabello

  3. Matematiska Institutionen, Stockholms Universitet, 106 91, Stockholm, Sweden

    Helena Granström

  4. Matematiska Institutionen, Linköpings Universitet, 581 83, Linköping, Sweden

    Jan-Åke Larsson

Authors
  1. Piotr Badzia̧g
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  2. Ingemar Bengtsson
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  3. Adán Cabello
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  4. Helena Granström
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  5. Jan-Åke Larsson
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Corresponding author

Correspondence to Ingemar Bengtsson.

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Badzia̧g, P., Bengtsson, I., Cabello, A. et al. Pentagrams and Paradoxes. Found Phys 41, 414–423 (2011). https://doi.org/10.1007/s10701-010-9433-3

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  • DOI: https://doi.org/10.1007/s10701-010-9433-3

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