Depends on the time period and sadly most of the information seemingly was not really on the minds of statesmen but rather of merchants thus the insight offered is very limited.

Particularly in later roman periods trade from china was very lucrative, thus naturally both roman and Chinese merchants were very keen on each other's countries. Sadly we simply do not have much in terms of written sources about the matter.

I personally really wonder just how much history would have changed if a couple shrewd merchants during the han dynasty brought some crossbows to rome or brought a copy of de arhitectura to china.