Haonan Zhang

activity

20202026

most citedQuantum Talagrand, KKL and Friedgut's theorems and the learnability of quantum Boolean functions

3 citations · 3 across the 7 of their papers we have counts for

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4 papers · 1 filter

math.OA2026

Sharp hypercontractivity for free group von Neumann algebras

Xinyuan Xie, Haonan Zhang

In this paper, we settle the problem of optimal hypercontractivity for free group von Neumann algebras. Namely, for $n \geq 2$ and the free group $F_{n}$ on $n$ generators, we…

math.OA2026

Sharp hypercontractivity for free orthogonal quantum groups of Kac type

Haonan Zhang

We prove that the normalized heat semigroup $P_{t} = e^{- t L}$ on every free orthogonal quantum group $O_{F}^{+}$ of Kac type satisfies hypercontractivity with the optimal time. More precis…

math.OA2021

Curvature-dimension conditions for symmetric quantum Markov semigroups

Melchior Wirth, Haonan Zhang

Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Ma…

math.OA2020

Complete gradient estimates of quantum Markov semigroups

Melchior Wirth, Haonan Zhang

In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which impli…