We introduce a framework to study discrete-variable (DV) quantum systems based on qudits.
It relies on notions of a mean state (MS), a minimal stabilizer-projection state (MSPS), and a …

Motivated by the three-dimensional topological field theory/two-dimensional conformal field
theory (CFT) correspondence, we study a broad class of one-dimensional quantum …

We introduce a quantum convolution and a conceptual framework to study states in discrete-
variable (DV) quantum systems. All our results suggest that stabilizer states play a role in DV …

Quantum Fourier analysis is a subject that combines an algebraic Fourier transform (pictorial
in the case of subfactor theory) with analytic estimates. This provides interesting tools to …

We establish an entropic, quantum central limit theorem and quantum inverse sumset
theorem in discrete-variable quantum systems describing qudits or qubits. Both results are …

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 …

We define a planar para algebra, which arises naturally from combining planar algebras
with the idea of Z _ N ZN para symmetry in physics. A subfactor planar para algebra is a …

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 for finite …

We introduce a new notion of an angle between intermediate subfactors and prove various
interesting properties of the angle and relate it to the Jones index. We prove a uniform $60 …

Jones introduced some unitary representations of Thompson group F constructed from a
given subfactor planar algebra, and all unoriented links arise as matrix coefficients of these …