Armen E. Allahverdyan, Roger Balian, Theo M. Nieuwenhuizen
To study ideal measurement processes involving a tested system S coupled to an apparatus A, we rely on a minimalist, statistical formulation of quantum mechanics, where states encode properties of ensembles. The required final state of S+A is shown to have a Gibbsian thermodynamic equilibrium form, not only for a large ensemble of runs, but also for arbitrary subensembles. This outcome is justified dynamically in quantum statistical mechanics as result of relaxation for models with suitably chosen interactions within A. The known quantum ambiguity which hinders the identification of physical subensembles is overcome owing to a specific relaxation process. The structure of the states describing the subsets of runs provides a frequency interpretation of Born's rule and explains the uniqueness of the result for each individual run, the so-called measurement problem.
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http://arxiv.org/abs/1303.7257
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