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Categorical characterizations of operator-valued measures - MaRDI portal

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Categorical characterizations of operator-valued measures

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Publication:4997275

zbMATH Open1467.81013arXiv1412.8528MaRDI QIDQ4997275

Author name not available (Why is that?)

Publication date: 29 June 2021

Abstract: The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert space. POVMs can equivalently be viewed as maps between effect algebras or as maps between algebras for the Giry monad. We will show that this equivalence is an instance of a duality between two categories. In the special case of continuous POVMs, we obtain two equivalent representations in terms of morphisms between von Neumann algebras.


Full work available at URL: https://arxiv.org/abs/1412.8528




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