Intersubjectivity as a principle determining physical observables and non-classicality

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.

Figures (3)

• Figure 1: Conceptual diagram of intersubjectivity. Two observers simultaneously perform the same measurement. (a) An intersubjective measurement guarantees identical outcomes for both observers, whereas (b) a generic measurement may produce random outcomes independently.
• Figure 2: Inclusion relation among the set of intersubjective (IS), completely intersubjective (CIS), and elementwise sharp (ES) measurements and the extreme points of the space of measurements (Ext) in (a) GPTs, (b) quantum theory and (c) classical theory.
• Figure S.1: Geometric illustration of the optimization problem in Proposition \ref{['intersubjectivity of unbiased measurement']}.

Theorems & Definitions (42)

• Definition 1
• Definition 2
• Theorem 1
• Theorem 2
• Definition 3
• Theorem 3
• Proposition 4
• Theorem 5
• Theorem 6
• proof : Proof of Theorem \ref{['intersubjective iff sharp']}