Transforming Particular Stabilizer Codes into Hybrid Codes

TL;DR

This paper demonstrates how to extend certain quantum stabilizer codes into hybrid codes that can transmit classical bits alongside quantum information in a qudit system, providing a method to find all subcodes and a lower bound on classical capacity.

Contribution

It introduces a procedure to transform stabilizer codes into hybrid codes with explicit subcode characterization and establishes a lower bound on classical information transmission in qudit hybrid codes.

Findings

Enables classical bits transmission in quantum stabilizer codes.

Provides an explicit method to find all subcodes of the hybrid code.

Establishes a lower bound of log2 p classical bits for qudit hybrid codes.

Abstract

In this paper, we prove how to extend a subset of quantum stabilizer codes into a qudit hybrid code storing $\log_2 p$ classical bits over a qudit space with dimension $p$, with $p$ prime. Our proof also gives an explicit procedure for finding the entire collection of stabilizer algebras for all of the subcodes of the hybrid code. This allows extra classical information to be transmitted without having to arduously search for additional codes and their associated codewords, and also provides a first lower bound to the amount of classical information able to be transmitted in a qudit hybrid code, but unfortunately only allows for $\log_2 p$ classical bits to be decoded by a receiver.