44 citations · 352 across the 42 of their papers we have counts for
43 papers
Entropy Contraction and Hypercontractivity for Gaussian Quantum Markov Semigroups
Zhengwei Liu, Jincheng Wan, Jinsong Wu
In this paper, we study finite-mode Gaussian quantum Markov semigroups with a faithful invariant Gaussian state. We present an algebraic characterization of the complete modified l…
Equivalence of states and bimodule quantum channels
Linzhe Huang, Chunlan Jiang, Zhengwei Liu +1
We study the action of quantum channels on states on a von Neumann algebra with conserved quantities encoded by a subalgebra . We define a phase as an eq…
3-Alterfolds and Quantum Invariants
Zhengwei Liu, Shuang Ming, Yilong Wang +1
In this paper, we introduce the concept of 3-alterfolds with embedded separating surfaces. When the separating surface is decorated by a spherical fusion category, we obtain quantu…
The Quantum Perron-Frobenius Space
Linzhe Huang, Arthur Jaffe, Zhengwei Liu +1
We introduce -positive elements in planar algebras. We establish the Perron-Frobenius theorem for -positive elements. We study the existence and uniquen…
Simulating Noisy Variational Quantum Algorithms: A Polynomial Approach
Yuguo Shao, Fuchuan Wei, Song Cheng +1
Large-scale variational quantum algorithms are widely recognized as a potential pathway to achieve practical quantum advantages. However, the presence of quantum noise might suppre…
Complete Positivity of Comultiplication and Primary Criteria for Unitary Categorification
Linzhe Huang, Zhengwei Liu, Sebastien Palcoux +1
In this paper, we investigate quantum Fourier analysis on subfactors and unitary fusion categories. We prove the complete positivity of the comultiplication for subfactors and deri…
Quantum convolution inequalities on Frobenius von Neumann algebras
Linzhe Huang, Zhengwei Liu, Jinsong Wu
In this paper, we introduce Frobenius von Neumann algebras and study quantum convolution inequalities. In this framework, we unify quantum Young's inequality on quantum symmetries…
Quantum smooth uncertainty principles for von Neumann bi-algebras
Linzhe Huang, Zhengwei Liu, Jinsong Wu
In this article, we prove various smooth uncertainty principles on von Neumann bi-algebras, which unify numbers of uncertainty principles on quantum symmetries, such as subfactors,…
Interpolated family of non group-like simple integral fusion rings of Lie type
Zhengwei Liu, Sebastien Palcoux, Yunxiang Ren
This paper is motivated by the quest of a non-group irreducible finite index depth 2 maximal subfactor. We compute the generic fusion rules of the Grothendieck ring of Rep(PSL(2,q)…
Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six
Zhengwei Liu, Sebastien Palcoux, Yunxiang Ren
This paper classifies the Grothendieck rings of complex fusion categories of multiplicity one up to rank six. Among 72 possible fusion rings, ones are filtered out by using ca…
The Grothendieck Ring of a Family of Spherical Categories
Zhengwei Liu, Christopher Ryba
The first author constructed a -parameterized spherical category $\sC$ over in [Liu15], whose simple objects are labelled by all Young diagrams. In this paper, w…
A Mathematical Picture Language Project
Arthur Jaffe, Zhengwei Liu
The mathematical picture language project that we began in 2016 has already yielded interesting results. We also point out areas of mathematics and physics where we hope that it wi…
Quantum Fourier Analysis
Arthur Jaffe, Chunlan Jiang, Zhengwei Liu +2
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides inte…
Quantized Graphs and Quantum Error Correction
Zhengwei Liu
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a m…
Fusion Bialgebras and Fourier Analysis
Zhengwei Liu, Sebastien Palcoux, Jinsong Wu
We introduce fusion bialgebras and their duals and systematically study their Fourier analysis. As an application, we discover new efficient analytic obstructions on the unitary ca…
Universal Quantum Computation by a Single Photon
Xiaoqin Gao, Zhengwei Liu
We use one photon to simulate an n-qubit quantum system for the first time. We propose a new scheme to realize universal quantum computation in polynomial time O(n^5). A generating…
Non-commutative Rényi Entropic Uncertainty Principles
Zhengwei Liu, Jinsong Wu
In this paper, we calculate the norm of the string Fourier transform on subfactor planar algebras and characterize the extremizers of the inequalities for parameters $0<p,q\leq \in…
Reflection Positivity and Levin-Wen Models
Arthur Jaffe, Zhengwei Liu
The reflection positivity property has played a central role in both mathematics and physics, as well as providing a crucial link between the two subjects. In a previous paper we g…
The adjoint braid arrangement as a combinatorial Lie algebra via the Steinmann relations
Zhengwei Liu, William Norledge, Adrian Ocneanu
We study a certain discrete differentiation of piecewise-constant functions on the adjoint of the braid hyperplane arrangement, defined by taking finite-differences across hyperpla…
De Finetti Theorems for Braided Parafermions
Kaifeng Bu, Arthur Jaffe, Zhengwei Liu +1
The classical de Finetti theorem in probability theory relates symmetry under the permutation group with the independence of random variables. This result has application in quantu…
Antisymmetric characters and Fourier duality
Zhengwei Liu, Jinsong Wu
Inspired by the quantum McKay correspondence, we consider the classical Lie theory as a quantum theory over . We introduce anti-symmetric characters for repr…
An angle between intermediate subfactors and its rigidity
Keshab Chandra Bakshi, Sayan Das, Zhengwei Liu +1
We introduce a new notion of angle between intermediate subfactors and prove various interesting properties of the angle and relate it with the Jones' index. We prove a uniform 60…
Lifting shadings on symmetrically self-dual subfactor planar algebras
Zhengwei Liu, Scott Morrison, David Penneys
In this note, we discuss the notion of symmetric self-duality of shaded planar algebras, which allows us to lift shadings on subfactor planar algebras to obtain Z/2Z-graded unitary…
A Mathematical Picture Language Program
Arthur Jaffe, Zhengwei Liu
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulati…