Changing the Local-Dimension of an Entanglement-Assisted Stabilizer Code Removes Entanglement Need

TL;DR

This paper demonstrates that by increasing the local dimension of entanglement-assisted stabilizer codes, the need for shared entanglement can be eliminated, simplifying the implementation of quantum error correction.

Contribution

It introduces a method to derive qudit codes from known codes, removing the requirement for shared entanglement in entanglement-assisted quantum error correction.

Findings

Elimination of entanglement requirement in certain quantum codes

Extension of code construction to higher-dimensional systems

Potential simplification for fault-tolerant quantum computing

Abstract

Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers. In this paper we show that codes for these systems can be derived from already known codes, and in particular this procedure removes the need for shared entanglement in entanglement-assisted quantum error-correcting codes, which is a result which could prove to be useful for fault-tolerant qudit, and even qubit, quantum computers.