[codethief]

I think we're talking past each other. :) I fully agree with your comment. However, I was addressing your original comment[0] about the naturalness of the tensor product. My whole point was merely (and maybe I didn't phrase it particularly well) that you need to assume all the stuff we (now) know about quantum mechanics (vector space structure etc.) in order to conclude that the tensor product is pretty much the only option you have. Your comment didn't mention this and seemed to make a much broader claim. That was all.

(EDIT: I think your other comment[1] fully resolves any gripe I had with your original comment. :))

[0]: https://news.ycombinator.com/item?id=37363347

[1]: https://news.ycombinator.com/item?id=37372225