  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.

Quantum Physics