Location of quantum information in additive graph codes

TL;DR

This paper investigates how quantum information is distributed across subsets of qudits in additive graph codes, using an operator-based framework called the information group to precisely characterize information localization.

Contribution

It introduces the information group concept and provides a detailed method to determine the presence of information in subsets of carriers within additive graph codes.

Findings

Characterization of information localization using the information group.

Explicit quantum circuit encoding for input information.

Partial trace analysis reveals subgroup isomorphisms.

Abstract

The location of quantum information in various subsets of the qudit carriers of an additive graph code is discussed using a collection of operators on the coding space which form what we call the information group. It represents the input information through an encoding operation constructed as an explicit quantum circuit. Partial traces of these operators down to a particular subset of carriers provide an isomorphism of a subgroup of the information group, and this gives a precise characterization of what kinds of information they contain. All carriers are assumed to have the same dimension D, an arbitrary integer greater than 1.