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”.