Be suprised. That whole Xinjiang Uygur Autonomus Region is covered with Caucasian skeletons and mummies that date to 2,000BC. The Chinese skeletons and mummies do not start to show up in that region until about 100BC. Here is a good book on the subject, it will be one on the best you've ever read.
"Are there any records of Chinese travellers in Rome or elsewhere in the Mediterranean during ancient times? I would be surprised if there are not, but I don't know the field."
I think the Han Dynasty sent an emissary to Rome in the early AD's.
"That whole Xinjiang Uygur Autonomus Region is covered with Caucasian skeletons and mummies that date to 2,000BC. The Chinese skeletons and mummies do not start to show up in that region until about 100BC."
VERY interesting. I'll read the book you are recommending.