Hilbert Space Representations of Decoherence Functionals and Quantum Measures - Quantum PhysicsReport as inadecuate




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Abstract: We show that any decoherence functional $D$ can be represented by a spanningvector-valued measure on a complex Hilbert space. Moreover, this representationis unique up to an isomorphism when the system is finite. We consider thenatural map $U$ from the history Hilbert space $K$ to the standard Hilbertspace $H$ of the usual quantum formulation. We show that $U$ is an isomorphismfrom $K$ 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 workto show that a quantum measure has a Hilbert space representation if and onlyif it is strongly positive. We also discuss classical decoherence functionals,operator-valued measures and quantum operator measures.



Author: Stan Gudder

Source: https://arxiv.org/







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