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We propose an approach to position measurements based on the hypothesis thatthe action of a position detector on a quantum system can be effectivelydescribed by a dissipative disordered potential. We show that such kind ofpotential is able, via the dissipation-induced Anderson localization, tocontemporary localize the wavefunction of the system and to dissipateinformation to modes bounded to the detector. By imposing a diabaticitycondition we demonstrate that the dissipative dynamics between the modes of thesystem leads to a localized energy exchange between the detector and the restof the environment -the "click" of the detector- thus providing a completedeterministic description of a position measurement. We finally numericallydemonstrate that our approach is consistent with the Born probability rule.

Localization by Dissipative Disorder: a Deterministic Approach to Position Measurements