Non-commutative graphs in the Fock space over one-particle Hilbert space

TL;DR

This paper explores non-commutative operator graphs in infinite-dimensional Fock spaces, focusing on their structure, examples generated by the Heisenberg-Weyl group, and implications for quantum error correction.

Contribution

It introduces specific examples of non-commutative graphs in Fock space and discusses quantum error correction within this framework.

Findings

Examples of non-commutative operator graphs generated by the Heisenberg-Weyl group.

Analysis of quantum error correction problems for these graphs.

Extension of previous studies to infinite-dimensional settings.

Abstract

In the present paper we continue our study of non-commutative operator graphs in infinite-dimensional spaces. We consider examples of the non-commutative operator graphs generated by resolutions of identity corresponding to the Heisenberg-Weyl group of operators acting on the Fock space over one-particle state space. The problem of quantum error correction for such graphs is discussed.