Block maps and Fourier analysis

Abstract

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 the Z 2 case, the asymptotic phenomenon of the block map coincides with that of that 2D Ising model. The study of block maps requires a further development of the recent work of the authors on the Fourier analysis of subfactors. We generalize the notion of sum set estimates in additive combinatorics for subfactors and prove the exact inverse sum set theorem. Using this new method, we characterize the extremal pairs of Young's inequality for subfactors, as well as the extremal operators of the Hausdorff-Young inequality.

Holographic software for quantum networks

“…Interesting inequalities related to uncertainty emerge from the last relation, see [42,56,43]. We describe these and other phenomena in quantum information by elementary pictures, which earlier diagrammatic approaches to quantum information did not capture naturally.…”

Quantum Fourier analysis

“…The limit points of the iteration of the block map are all biprojections for finite-index, irreducible subfactors (47). We regard this result as a quantum 2D central limit theorem.…”

Non-commutative Rényi entropic uncertainty principles

“…We refer the reader to [18] for the definition of subfactor planar algebras and keep the notations in [16]. Suppose P • = {P n,± } n≥0 is a subfactor planar algebra.…”

“…C. Jiang and the authors completely characterize the extremizers of the Hausdorff-Young inequality: [16]). Suppose P • is an irreducible subfactor planar algebra.…”

“…This paper is organized as follows. In Section 2, we recall some results in [14,16] on the Fourier analysis for subfactor planar algebras. In Section 3, we calculate the norm of the Fourier transform on subfactor planar algebras and find all extremizers.…”