atyy, bill.. I think there is a mistake inside the paper above.. specifically in section 1.2.3 where:
"However, note that even though 2 = 3, their physical interpretation is not
quite the same. System 2 is in a definite deterministic physical state, whereas
system 3 is part of a composite superposition state. Its physical state is truly
undetermined, as long as no measurement is performed on \part B" of system
3 (that we removed from our control). System 2 is said to be a proper mixture,
versus system 3 which is in a improper mixture. When a measurement
is performed on the discarded part B of system 3, but we are not told of the
outcome (ignorance), system 3 reduces to a proper mixture, and systems 2 and
3 are then physically identical."
The mistake is for system 3 to reduce to a proper mixture.. there is a collapse somewhere.. whereas in system 2.. tere is no issue of collapse.. so how can they be physically identical?