44 citations · 352 across the 42 of their papers we have counts for
21 papers · 1 filter
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…
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…
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,…
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…
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…
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…
Block maps and Fourier analysis
Changlan Jiang, Zhengwei Liu, Jinsong Wu
We introduce block maps for subfactors and study their dynamic systems. We prove that the limit points of the dynamic system are positive multiples of biprojections and zero. For t…
Jones-Wassermann subfactors for modular tensor categories
Zhengwei Liu, Feng Xu
The representation theory of a conformal net is a unitary modular tensor category. It is captured by the bimodule category of the Jones-Wassermann subfactor. In this paper, we cons…
Young's inequality for locally compact quantum groups
Zhengwei Liu, Simeng Wang, Jinsong Wu
In this paper, we generalize Young's inequality for locally compact quantum groups and obtain some results for extremal pairs of Young's inequality and extremal functions of Hausdo…
Classification of Thurston-relation subfactor planar algebras
Corey Jones, Zhengwei Liu, Yunxiang Ren
Bisch and Jones suggested the skein theoretic classification of planar algebras and investigated the ones generated by 2-boxes with the second author. In this paper, we consider 3-…
Uncertainty Principles for Kac Algebras
Zhengwei Liu, Jinsong Wu
In this paper, we introduce the notation of bi-shift of biprojections in subfactor theory to unimodular Kac algebras. We characterize the minimizers of Hirschman-Beckner uncertaint…
The generator conjecture for subfactor planar algebras
Zhengwei Liu, David Penneys
We state a conjecture for the formulas of the depth 4 low-weight rotational eigenvectors and their corresponding eigenvalues for the subfactor planar algebras. We prove the c…
Yang-Baxter relation planar algebras
Zhengwei Liu
We give a new type of Schur-Weyl duality for the representations of a family of quantum subgroups and their centralizer algebra. We define and classify singly-generated, Yang-Baxte…
Singly generated planar algebras of small dimension, Part III
Dietmar Bisch, Vaughan F. R. Jones, Zhengwei Liu
The first two authors classified subfactor planar algebra generated by a non-trivial 2-box subject to the condition that the dimension of 3-boxes is at most 12 in Part I; 13 in Par…
Noncommutative Uncertainty Principles
Chunlan Jiang, Zhengwei Liu, Jinsong Wu
The classical uncertainty principles deal with functions on abelian groups. In this paper, we discuss the uncertainty principles for finite index subfactors which include the cases…
1-supertransitive subfactors with index at most 6+1/5
Zhengwei Liu, Scott Morrison, David Penneys
We classify irreducible II_1 subfactors A \subset B such that B \ominus A is reducible as an A-A bimodule, with index at most 6+1/5, leaving aside the composite subfactors at index…
Composed inclusions of and subfactors
Zhengwei Liu
In this article, we classify all standard invariants that can arise from a composed inclusion of an with an subfactor. More precisely, if $\mathcal{N}\subset \mathcal{P…
Exchange relation planar algebras of small rank
Zhengwei Liu
The main purpose of this paper is to classify exchange relation planar algebras with 4 dimensional 2-boxes. Besides its skein theory, we emphasize the positivity of subfactor plana…