Multiboson Logical Operators, Laughlin States, and Virasoro Algebra

TL;DR

This paper explores the deep mathematical structures linking multi-boson logical operators, Laughlin states, and the Virasoro algebra, revealing their roles in quantum information encoding and topological quantum field theories.

Contribution

It introduces a novel analysis of multi-boson logical operators and their relation to the Virasoro algebra and fractional quantum Hall states, connecting quantum information and topological physics.

Findings

Logical operators constructed from multi-bosons relate to the Virasoro algebra.

Connections established between quantum Hall states and diffeomorphism algebra.

Insights into encoding information in topologically ordered systems.

Abstract

Leading idea of this manuscript is to discuss the structure and the deep correlations among different quantum physical systems, and to explore how such correlations bear on the capacity of the systems to encode and manipulate information. In particular, the role of logical operators constructed out of multi-boson (and possibly fractionary-boson) operators is analyzed in its relation on the one hand with the algebra of diffeomorphisms of the circle, on the other with the physical properties of the fractional quantum Hall effect (described in terms of Laughlin states) and of its many electron representation in terms of the Chern-Simons topological quantum field theory.