Title: Hilbert Space Representations of Decoherence Functionals and Quantum Measures
Abstract: We show that any decoherence functional $D$ can be represented by a spanning vector-valued measure on a complex Hilbert space. Moreover, this representation is unique up to an isomorphism when the system is finite. We consider the natural map $U$ from the history Hilbert space $K$ to the standard Hilbert space $H$ of the usual quantum formulation. We show that $U$ is an isomorphism from $K$ onto a closed subspace of $H$ and that $U$ is an isomorphism from $K$ onto $H$ if and only if the representation is spanning. We then apply this work to show that a quantum measure has a Hilbert space representation if and only if it is strongly positive. We also discuss classical decoherence functionals, operator-valued measures and quantum operator measures.
Publication Year: 2010
Publication Date: 2010-11-08
Language: en
Type: preprint
Access and Citation
Cited By Count: 1
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot