Quantum Measurement as Marginalization and Nested Quantum Systems

Abstract: In prior work, we have shown how the basic concepts and terms of quantum mechanics relate to factorizations and marginals of complex-valued quantum mass functions, which are generalizations of joint probability mass functions. In this paper, using quantum mass functions, we discuss the realization of measurements in terms of unitary interactions and marginalizations. It follows that classical measurement results strictly belong to local models, i.e., marginals of more detailed models. Classical variables that are created by marginalization do not exist in the unmarginalized model, and different marginalizations may yield incompatible classical variables. These observations are illustrated by the Frauchiger-Renner paradox, which is analyzed (and resolved) in terms of quantum mass functions. Throughout, the paper uses factor graphs to represent quantum systems/models with multiple measurements at different points in time.