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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/3996

Title: On extending the quantum measure
Authors: Dowker, Fay
Johnston, Steven
Surya, Sumati
Issue Date: 17-Dec-2010
Publisher: IOP Publishing Ltd.
Citation: Journal of Physics A, 2010, Vol. 43, p505305
Abstract: We point out that a quantum system with a strongly positive quantum measure or decoherence functional gives rise to a vector-valued measure whose domain is the algebra of events or physical questions. This gives an immediate handle on the question of the extension of the decoherence functional to the sigma algebra generated by this algebra of events. It is on the latter that the physical transition amplitudes directly give the decoherence functional. Since the full sigma algebra contains physically interesting questions, like the return question, extending the decoherence functional to these more general questions is important. We show that the decoherence functional, and hence the quantum measure, extends if and only if the associated vector measure does. We give two examples of quantum systems whose decoherence functionals do not extend: one is a unitary system with finitely many states, and the other is a quantum sequential growth model for causal sets. These examples fail to extend in the formal mathematical sense and we speculate on whether the conditions for extension are unphysically strong.
Description: Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI: http://hdl.handle.net/2289/3996
ISSN: 1751-8113
1751-8121-(Online)
Alternative Location: http://arxiv.org/abs/1007.2725
http://iopscience.iop.org/1751-8121/43/50/505305/
http://adsabs.harvard.edu/abs/2010JPhA...43X5305D
Copyright: 2010 IOP Publishing Ltd.
Appears in Collections:Research Papers (TP)

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