Recursive Quantum Qudit Convolutional Codes Need Not be Catastrophic

TL;DR

This paper demonstrates that recursive quantum qudit convolutional codes can be non-catastrophic when the qudit dimension is a prime larger than 2, opening new avenues for quantum turbo code development.

Contribution

It proves that the no-go theorem for catastrophic recursive quantum convolutional codes does not hold for prime-dimensional qudits, enabling new quantum turbo code designs.

Findings

Recursive quantum qudit codes can be non-catastrophic for prime dimensions > 2

Extending to qudit space removes previous limitations on quantum convolutional codes

Stimulates further research into quantum turbo coding schemes

Abstract

Classical turbo codes efficiently approach the Shannon limit, and so bringing these over to the quantum scenario would allow for rapid transmission of quantum information. Early on in the work of defining the quantum analogue, it was shown that an efficient recursive subroutine (quantum convolutional codes) would always be catastrophic. This result may have stunted the further research into this coding scheme. In this document, we prove that this previously proven no-go theorem is no longer always true if we extend the coding scheme into qudit space with dimension some prime larger than 2. This removes a blockade in the development of quantum turbo codes and hopefully will stimulate further research in this area.