Ozawa’s Intersubjectivity Theorem as Objection to QBism Individual Agent Perspective

Abstract

QBism’s foundational statement that “the outcome of a measurement of an observable is personal” is in the straight contraversion with Ozawa’s Intersubjectivity Theorem (OIT). The latter (proven within the quantum formalism) states that two observers, agents within the QBism terminology, performing joint measurements of the same observable A on a system S in the state ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi $$\\end{document} should get the same outcome A=x.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A=x.$$\\end{document} In Ozawa’s terminology, this outcome is intersubjective and it can’t be treated as personal. This is the strong objection to QBism which can’t survive without updating its principles. The essential aspect in understanding of the OIT-impact on QBism’s foundations takes the notion of quantum observable. This paper comprises the complementary discussion highlighting the difference between the accurate, von Neumann, and inaccurate, noisy, quantum observables which are represented by PVMs and POVMs respectively. Moreover, we discuss the OIT-impact on the Copenhagen interpretation of quantum mechanics.