A cb-Bohnenblust–Hille inequality with constant one and its applications in learning theory
Abstract The main result of this work shows that Bohnenblust–Hille inequality for m -homogeneous polynomials holds with constant one when the infinity norm is replaced by the completely bounded norm. Moreover, we show that this inequality finds some interesting consequences in quantum learning theory. In the second part of this paper, we broaden our investigation of the Bohnenblust–Hille inequality to other contexts. In particular, we extend recent results by Volberg and Zhang, demonstrating its applicability within a framework we have termed “Learning Low-Degree Quantum Objects”.
Authors
- Arkopal Dutt
- Carlos Palazuelos (ORCID: https://orcid.org/0000-0002-3218-855X)
- Srinivasan Arunachalam (ORCID: https://orcid.org/0000-0002-1338-8169)
- Francisco Escudero (ORCID: https://orcid.org/0000-0001-5982-1127)
Institutions
- IBM (United States) (US)
- University of Illinois Urbana-Champaign (US)
- QuSoft (NL)
- Institute of Mathematical Sciences (ES)
Publication Details
- Journal
- Mathematische Annalen
- Published
- 2025-05-06
- DOI
- https://doi.org/10.1007/s00208-025-03142-5
- Primary Topic
- Mathematical Analysis and Transform Methods
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Comunidad de Madrid
- European Commission
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Ministerio de Ciencia e Innovación
- Agencia Estatal de Investigación
- HORIZON EUROPE Marie Sklodowska-Curie Actions