ach other.
If
Gan Ying's 97CE mission to Rome had succeeded, could it have formed the basis of a more concrete relationship between the two empires? What did Rome and Han have to learn from each other and could their peaks have lasted longer than they did in OTL as a result of their communication?
China and Rome were particularily far from each other : a good part of Gan Ying's failure was that he crossed all Asia, and Persians tricked him telling there was as much way to do.
But even without trickery/bribery?, it's a long way to go.
Remember that Rome knew of India, which was half-way, and only but rarely sent embassies to local princes or these princes sending embassies to Rome, even when there were strategic reasons doing so, part of these embassies possibly coming from Kushans.
Not that you didn't have contacts, there's proofs of the contrary, but these essentially outreached the political projection capacities of the empire. So, China, twice as much further...
It counts for China as well : "Da Qin" was at best a really vague idea, as much that "Serica" was for Romans : there's something on the other edge of the world we know, probably, exists.
Which let contacts with traders, Romans in the sense they were part of Romania but generally Hellenes or Egyptians culturally (as hinted by the roman trade goods found in eastern Asia) : giving that Indian technologies didn't were borrowed trough trade, but progressive military usage (Kushans to Persians, Persians to Arabs, Arabs to Latins, etc.) in West, such as steel metallurgy; I'm not confident in the chances of merchants pulling it in China : they would probably consider paper as a curiosity.
Does that means you couldn't have more than this IATL? Well, I wouldn't go that far. Romans emperors were victims of Alexander's Syndroma on a large scale, and even if an outright conquest of Persia is out of question on any plausible TL, a non-antagonized Persia, with more neutral or pro-Roman client kings, could be a better stepstone to Asia.
IOTL not only merchant interests but political principles neutralized Silk Roads for Romans, ITTL maybe terrestrial contacts could exists, meaning more contacts not with China directly but with empires and populations that are.
I doubt you'd have much out of it, tough : Indian cultures didn't borrowed paper from China but from Arabo-Islamic world, for instance.
Apart from really bankable trade goods, I doubt you'd have much more than more geographical precision, and maybe political treaties about "these people are doing it well, and emperors should do the same there" that would be far less about reality, than idealization of the quasi-unknown.
China and Rome are simply too far from each other. It asked, for actual European/Chinese contacts, the existence of a political continuum between China and Russia/Anatolia.
For anything more, you'd probably need to pull an ancient equivalent to Pax Mongolica.