The Born rule from a consistency requirement on hidden measurements in complex Hilbert space
arXiv:quant-ph/0212151
Abstract
We formalize the hidden measurement approach within the very general notion of an interactive probability model. We narrow down the model by assuming 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.
10 pages, no figures, accepted for publication in Int. J. Theor. Phys