The Born Rule from a Consistency Requirement on Hidden Measurements in Complex Hilbert Space
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We formalize the hidden measurement approach within the very general notion of an interactive probability model. We narrow down the model by assuming that the state space of a physical entity is a complex Hilbert space and introduce the principle of consistent interaction which effectively partitions the space of apparatus states. The normalized measure of the set of apparatus states that interact with a pure state giving rise to a fixed outcome is shown to be in accordance with the probability obtained using the Born rule.
KeywordsBorn rule hidden measurements interactive probability model
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