3 citations · 3 across the 7 of their papers we have counts for
8 papers
Tightness of and counterexamples to several quantum estimates
Joseph Slote, Alexander Volberg, Haonan Zhang
We prove here several tightness results for such quantum inequalities as 1) the comparison of operator norm and product norm of -local hamiltonians, 2) Bohnenblust--Hille inequa…
The estimates for Boolean surface area of polynomial threshold functions
Fan Chang, Joseph Slote, Alexander Volberg +2
Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work o…
Approximating the operator norm of local Hamiltonians via few quantum states
Lars Becker, Joseph Slote, Alexander Volberg +1
Consider a Hermitian operator acting on a complex Hilbert space of dimension . We show that when has small degree in the Pauli expansion, or in other words, is a l…
Fourier growth of degree polynomials
Lars Becker, Joseph Slote, Alexander Volberg +1
We prove bounds for the absolute sum of all level- Fourier coefficients for , where polynomial is of degree or degree .
Noncommutative Bohnenblust--Hille Inequality for qudit systems
Joseph Slote, Alexander Volberg, Haonan Zhang
Previous noncommutative Bohnenblust--Hille (BH) inequalities addressed operator decompositions in the tensor-product space ; \emph{i.e.,} for systems o…
A dimension-free discrete Remez-type inequality on the polytorus
Joseph Slote, Alexander Volberg, Haonan Zhang
Consider a function from the -fold product of multiplicative cyclic groups of order . Any such may be extended via its Fourier expansion to an an…
Bohnenblust--Hille inequality for cyclic groups
Joseph Slote, Alexander Volberg, Haonan Zhang
For any and the multiplicative cyclic group of order , consider any function and its Fourier expansion $f(z)=\sum_{α\in\{0,1,\ldots,K-1\}^n}a_…
Quantum and classical low-degree learning via a dimension-free Remez inequality
Ohad Klein, Joseph Slote, Alexander Volberg +1
Recent efforts in Analysis of Boolean Functions aim to extend core results to new spaces, including to the slice , the hypergrid , and noncommutative spaces…