The relationship between QCMA and QMA in the Turing and Communication model

First my background about computational complexity is still beginner.

Recent paper published by Klauck and Podder [KP14] show that for the first time an exponential gap between computing partial Boolean functions in a QCMA and QMA in communication model. However, Aharonov and Naveh [AN02] conjecture that QMA = QCMA in the Turing model.

[KP14] state the following open problem:

Thus, in order to show that QCMA = QMA; we need nonalgebrizing techniques.

I just don’t understand how they relate the communication model with the Turing model?

According to my understanding is that communication model is different than Turing model. that is, we have different results, proofs, etc. therefore, [KP14] argue that any separation in the two-way communication model would imply using non-algebrizing techniques, how could it be?

thanks in advance