I thought the point was that they can't perfectly share information. So, they could both zero knowledge proof their way through "we share common knowledge" but

I thought the point was that they can't perfectly share information. So, they could both zero knowledge proof their way through "we share common knowledge" but be unable to directly prove it due to a halting problem. I agree that this write up is missing some key details, but grokking the publication will take a few weeks/months. Disclaimer: zero quantum research background, only cs and a hint of math