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Quantum Operads

In: Dialogues Between Physics and Mathematics

Author

Listed:
  • Noémie Combe

    (Max Planck Institute for Mathematics in the Sciences)

  • Yuri I. Manin

    (Max Planck Institute for Mathematics)

  • Matilde Marcolli

    (Caltech, Mathematics Department)

Abstract

The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated by physics, or information theory etc., the respective symmetry objects might become more sophisticated such as quasigroups, loops, quantum groups. In this paper, we introduce and study quantum symmetries of very general categorical structures: operads. Its initial motivation were spaces of probability distributions on finite sets. We also investigate here how structures of quantum information, such as quantum states and some constructions of quantum codes, are algebras over operads.

Suggested Citation

  • Noémie Combe & Yuri I. Manin & Matilde Marcolli, 2022. "Quantum Operads," Springer Books, in: Mo-Lin Ge & Yang-Hui He (ed.), Dialogues Between Physics and Mathematics, chapter 0, pages 113-145, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-17523-7_5
    DOI: 10.1007/978-3-031-17523-7_5
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