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.
Dedicated to C. N. Yang
... esta selva selvaggia e aspra e forte che nel pensier rinova la paura ... Dante Alighieri, Inferno, Canto 1
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Acknowledgements
NC was supported by a Minerva grant, hosted at the Max Planck Institute for Mathematics in the Sciences; MM was supported by NSF grant DMS-2104330.
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Combe, N., Manin, Y.I., Marcolli, M. (2022). Quantum Operads. In: Ge, ML., He, YH. (eds) Dialogues Between Physics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-031-17523-7_5
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DOI: https://doi.org/10.1007/978-3-031-17523-7_5
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