  Pusey, Barrett and Rudolph (PBR) have recently given a completely novel
argument that restricts the class of possible models for quantum phenomena
(arXiv:1111.3328). In these notes the assumptions used by PBR are considerably
weakened, to further restrict the class of possible models. The
`factorisability' assumption used by PBR is replaced by a far weaker
`compatibility' assumption for uncorrelated quantum subsystems which, moreover,
does not require the assignation of separate underlying properties to each
subsystem (i.e, reductionism). Further, it is shown that an assumption of
measurement independence may be dropped to obtain a related result having the
same experimental significance (at the expense of a weaker conceptual
significance). The latter is a remarkable feature of the PBR approach, given
that Bell inequalities, steering inequalities and Kochen-Specker theorems all
require an assumption of this type.
