Intersubjectivity as a principle determining physical observables and non-classicality

TL;DR

This paper introduces an operational principle based on intersubjectivity that characterizes quantum observables and classicality, linking measurement theory with information processing tasks.

Contribution

It reformulates Ozawa's intersubjectivity condition within generalized probabilistic theories and characterizes PVMs and classical systems through intersubjectivity preservation.

Findings

A POVM is a PVM iff all its coarse-grainings are intersubjective.

A system is classical iff intersubjectivity is preserved under any coarse-graining.

Measurements with intersubjectivity support state tomography and discrimination.

Abstract

We identify an operational principle that singles out Projection-Valued Measures (PVMs) among general Positive Operator-Valued Measures (POVMs), bridging the modern quantum measurement theory and the traditional formulation based on projective measurements of physical observables. We reformulate Ozawa's intersubjectivity condition, which requires inter-observer agreement of the measurement outcomes, in a quantitative manner within the framework of generalized probabilistic theories. We prove that (i) a POVM is a PVM if and only if its every coarse-graining is intersubjective, and (ii) a system is classical if and only if intersubjectivity is preserved under any coarse-graining, establishing a complete characterization of the physical observables and the classical theory. Furthermore, measurements with intersubjectivity are sufficiently rich for the informational tasks of state tomography and state discrimination, testifying to its operational significance in quantum and beyond information processing.