Abstract

The measurement postulates specify: the mathematical structure of quantum measurements (Hermitian operators, POV Ms), the formula for assigning outcome probabilities (Born’s rule) and the post-measurement state-update rule. The rest of postulates are often referred to as “unitary quantum mechanics”. We characterise the family of theories consisting of unitary quantum mechanics supplemented with non-quantum measurement postulates; and prove that any such theory has the following problematic feature: the set of mixed state of any finite-dimensional Hilbert space has infinite dimension, which makes the task of state estimation impossible. Therefore, if we disregard theories with this problematic feature then the only measurement postulates compatible with unitary quantum mechanics are the good old quantum measurement postulates. This result reveals the true identity of the “measurement postulates” as “measurement theorems”.