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Motivated by recent experiments on quantum trapped fields, we give a rigorousproof that repeated indirect quantum non-demolition (QND) measurements convergeto the collapse of the wave function as predicted by the postulates of quantummechanics for direct measurements. We also relate the rate of convergencetoward the collapsed wave function to the relative entropy of each indirectmeasurement, a result which makes contact with information theory.

Convergence of repeated quantum non-demolition measurements and wave function collapse