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A Fixed Point Result for Environment-Induced Semigroups

A. M. Lisewski
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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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A. M. Lisewski. 2002-11-30. A Fixed Point Result for Environment-Induced Semigroups. https://arxiv.org/abs/quant-ph/0211054

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