dorsal/arxiv
View SchemaA Fixed Point Result for Environment-Induced Semigroups
| Authors | A. M. Lisewski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211054 |
| URL | https://arxiv.org/abs/quant-ph/0211054 |
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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"abstract": "Based on the environment induced semigroup approach to the quantum\nmeasurement process, we show that a certain class of these semigroups, referred\nto as contractive uniformly $k$-Lipschitzian semigroups, exhibit a fixed point\nproperty. With regard to the quantum measurement problem, semigroups of this\nkind ensure decoherence and the selection of a single state from the familiy of\npointer states. In fact, the common fixed point is the selected state.",
"arxiv_id": "quant-ph/0211054",
"authors": [
"A. M. Lisewski"
],
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"title": "A Fixed Point Result for Environment-Induced Semigroups",
"url": "https://arxiv.org/abs/quant-ph/0211054"
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