论文标题
非交换性的bohnblust-纤维不平等
Noncommutative Bohnenblust--Hille inequalities
论文作者
论文摘要
Bohnnblust-布尔立方体的hille不平等现象已经证明了无尺寸常数，这些常数在\ cite \ cite {Defant2019Fourier}中呈较高的指数。这种不平等在学习低度布尔函数方面发现了很棒的应用\ cite {eskenazis2022Learning}。通过学习量子可观察的动机，\ cite {rwz22}的量子类似物的量子类似物 - 希尔布斯特的不平等现象。猜想是在\ cite {chp}中解决的。在本文中，我们给出了这些Bohnenblust的新证明 - Qubit系统的基础不平等现象，其常数为无维且程度的指数增长。结果，我们获得了低度多项式的Junta定理。使用类似的想法，我们还研究了低度量子可观察物的学习问题，以及在量子布尔立方体上的Bohr半径现象。
Bohnenblust--Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree \cite{defant2019fourier}. Such inequalities have found great applications in learning low-degree Boolean functions \cite{eskenazis2022learning}. Motivated by learning quantum observables, a qubit analogue of Bohnenblust--Hille inequality for Boolean cubes was recently conjectured in \cite{RWZ22}. The conjecture was resolved in \cite{CHP}. In this paper, we give a new proof of these Bohnenblust--Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr's radius phenomenon on quantum Boolean cubes.
