Ozawa's Intersubjectivity Theorem as justification of RQM's postulate on internally consistent descriptions

TL;DR

This paper argues that Ozawa's Intersubjectivity Theorem provides a rigorous bridge between quantum measurement theory and Relational Quantum Mechanics by showing that, for measurements that satisfy probability reproducibility and are represented by von Neumann observables, different observers can obtain intersubjectively consistent results. It details how PVM-based measurements lead to exact agreement via $P(M_1(T)=x, M_2(T)=y|\\psi\\xi_1\\xi_2)=\\delta(x-y) \\|E(x)\\psi\\|^2$, and how generalized POVMs can undermine this if not probability-reproducible. The work then maps von Neumann's measurement formalism onto Rovelli's notion of an observer by treating 'observer' as any physical system and introducing the A1A2-entanglement for compatible observables to reproduce the correlation structure of measurements. It further discusses the matching between VN's and RQM's postulates, particularly Postulate 5 and 6, and clarifies the conditions under which cross-perspective consistency is guaranteed. Overall, the paper strengthens the grounding of RQM in quantum measurement theory while clarifying the limits imposed by generalized measurements and the interpretation of 'same basis'.

Abstract

The Ozawa's Intersubjectivity Theorem (OIT) proved within quantum measurement theory supports the new postulate of relational quantum mechanics (RQM), the postulate on internally consistent descriptions. We remark that this postulate was proposed only recently to resolve the problem of intersubjectivity of information in RQM. In contrast to RQM for which OIT is a supporting theoretical statement, QBism is challenged by OIT.