Response to "The measurement postulates of quantum mechanics are not redundant"

TL;DR

This paper defends the original result that quantum measurement postulates can be derived from other postulates, by showing that proposed counterexamples violate key quantum principles such as pure state structure and finite-dimensionality.

Contribution

We refute Kent's critique by demonstrating that his theories violate fundamental quantum assumptions, reaffirming the derivability of measurement postulates from other quantum postulates.

Findings

Kent's theories contain non-Hilbert pure states

His theories violate finite-dimensionality of mixed states

The critique does not hold under quantum principles

Abstract

Adrian Kent has recently presented a critique [arXiv:2307.06191] of our paper [Nat. Comms. 10, 1361 (2019)] 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 [Nat. Comms. 10, 1361 (2019)] 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.