Response to “The measurement postulates of quantum mechanics are not redundant”

Adrian Kent has recently presented a critique [1] of our paper [2] in which he claims to refute our main result: the measurement postulates of quantum mechanics can be derived from the rest of postulates, once we assume that the set of mixed states of a finite-dimensional Hilbert space is finite-dimensional. To construct his argument, Kent considers theories resulting from supplementing quantum mechanics with hypothetical ``post-quantum'' measurement devices. We prove that each of these theories contains pure states (i.e. states of maximal knowledge) which are not rays of the Hilbert space, in contradiction with the ``pure state postulate'' of quantum mechanics. We also prove that these alternatives violate the finite-dimensionality of mixed states. Each of these two facts separately invalidates the refutation. In this note we also clarify the assumptions used in [2] and discuss the notions of pure state, physical system, and the sensitivity of the structure of the state space under modifications of the measurements or the dynamics.