I have read the introduction (only cursorily). What bothers me is that they may be conflating C as C-vector space, which is R (as R-vector space) tensor C (com

I have read the introduction (only cursorily). What bothers me is that they may be conflating C as C-vector space, which is R (as R-vector space) tensor C (complex dim 1). with R^2 as R-vector space, tensored by C (complex dim 2). Because when they "add a real qubit", they seem to be adding a degree of freedom which you do not have when you have just one C-qubit. But -I repeat- I have only looked over the intro.