Quantum Operads

Noémie Combe, Yuri I. Manin () and Matilde Marcolli
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Noémie Combe: Max Planck Institute for Mathematics in the Sciences
Yuri I. Manin: Max Planck Institute for Mathematics
Matilde Marcolli: Caltech, Mathematics Department

Chapter Chapter 5 in Dialogues Between Physics and Mathematics, 2022, pp 113-145 from Springer

Abstract: 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.

Keywords: Information spaces; Moufang loops; Monoidal categories; Operads; Monoids; Magmas (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-17523-7_5

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DOI: 10.1007/978-3-031-17523-7_5

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