Quantum Measurement as Marginalization and Nested Quantum Systems
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Measurements in quantum mechanics can be derived from unitary interactions and marginalizations. In this setting, the "collapse of the wavefunction" becomes a mathematical fact that depends on a condition. The consequences of severe violations of this condition are illustrated by the Frauchiger-Renner paradox. Deriving measurement from marginalized unitary interactions further implies that classical variables exist only within some scope or frame of reference: classical variables that are created by marginalization do not exist in the unmarginalized system, and different marginalizations may yield incompatible classical variables. Again, these observations are illustrated by the Frauchiger-Renner paradox. Throughout, the paper heavily uses factor graphs to represent quantum systems with multiple measurements at different points in time.
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