Algebras of Measurements: the logical structure of Quantum Mechanics
<|reference_start|>Algebras of Measurements: the logical structure of Quantum Mechanics: In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute. Keywords: Quantum measurements, Measurement algebras, Quantum Logic. PACS: 02.10.-v.<|reference_end|>
@article{lehmann2005algebras,
    title={Algebras of Measurements: the logical structure of Quantum Mechanics},
    author={Daniel Lehmann, Kurt Engesser and Dov M. Gabbay},
    journal={International Journal of Theoretical Physics, 45(4) April 2006,
  pages 698-723},
    year={2005},
    doi={10.1007/s10773-006-9062-y},
    number={TR 2005-91 Leibniz Center for Research in Computer Science, Hebrew
  Un. Jerusalem},
    archivePrefix={arXiv},
    eprint={quant-ph/0507231},
    primaryClass={quant-ph cs.AI}
}