44 citations · 96 across the 20 of their papers we have counts for
21 papers
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…
Intertwining Properties for Bimodule Quantum Markov Semigroups
Chunlan Jiang, Jincheng Wang, Jinsong Wu
In this paper, we study the Bakry-Émery estimates for GNS- and KMS-symmetric semigroups in terms of the Fourier multiplier of the gradient form and the iterated gradient form in th…
Alterfold Theory and Topological Modular Invariance
Zhengwei Liu, Shuang Ming, Yilong Wang +1
We propose a topological paradigm in alterfold topological quantum field theory to explore various concepts, including modular invariants, -induction and connections in Morita c…
Phase Group Categories of Bimodule Quantum Channels
Linzhe Huang, Chunlan Jiang, Zhengwei Liu +1
In this paper, we study the quantum channel on a von Neuamnn algebra preserving a von Neumann subalgebra , namely an --bimodule…
Alterfold Topological Quantum Field Theory
Zhengwei Liu, Shuang Ming, Yilong Wang +1
We introduce the 3-alterfold topological quantum field theory (TQFT) by extending the quantum invariant of 3-alterfolds. The bases of the TQFT are explicitly characterized and the…
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…
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…
Similarity Invariants of Essentially normal Cowen-Douglas Operators and Chern Polynomials
Chunlan Jiang, Kui Ji, Jinsong Wu
In this paper, we systematically study a class of essentially normal operators by using the geometry method from the Cowen-Douglas theory and prove a Brown-Douglas-Fillmore theorem…
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…
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…
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…
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…
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…
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…
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…
Mbius Disjointness for Exact C Algebras
Jinsong Wu, Wei Yuan
In this paper we introduce the Möbius disjointness for C-algebras with their automorphisms and studied the Möbius disjointness for finite dimensional C algebras, finite von…