A Fixed Point Result for Environment-Induced Semigroups
A. M. Lisewski
Abstract
Based on the environment induced semigroup approach to the quantum measurement process, we show that a certain class of these semigroups, referred to as contractive uniformly k-Lipschitzian semigroups, exhibit a fixed point property. With regard to the quantum measurement problem, semigroups of this kind ensure decoherence and the selection of a single state from the familiy of pointer states. In fact, the common fixed point is the selected state.
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