Lahti, Pekka J.; Mączynski, Maciej J. Partial order of quantum effects. (English) Zbl 0829.46060 J. Math. Phys. 36, No. 4, 1673-1680 (1995). The authors examine the order structure of the set of effects and some of its subsets. They show: The set of effects is not a lattice with respect to its natural order. Projection operators do have the greatest lower bounds (and the least upper bounds) in that set, but there are also other (incomparable) effects which share this property. However, the coexistence, the commutativity, and the regularity of a pair of effects are not sufficient for the existence of their infima and suprema. The structure of the range of an observable (as a normalized POV measure) can vary from that of a commutative Boolean to a noncommutative non-Boolean subset of effects. Cited in 1 ReviewCited in 20 Documents MSC: 46N50 Applications of functional analysis in quantum physics 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) Keywords:set of effects; coexistence; commutativity; regularity; normalized POV measure PDFBibTeX XMLCite \textit{P. J. Lahti} and \textit{M. J. Mączynski}, J. Math. Phys. 36, No. 4, 1673--1680 (1995; Zbl 0829.46060) Full Text: DOI References: [1] DOI: 10.2307/2372173 · Zbl 0042.35001 · doi:10.2307/2372173 [2] DOI: 10.2307/2372173 · Zbl 0042.35001 · doi:10.2307/2372173 [3] DOI: 10.1007/BF00672820 · Zbl 0806.03040 · doi:10.1007/BF00672820 [4] DOI: 10.1090/S0002-9947-1965-0206736-3 · doi:10.1090/S0002-9947-1965-0206736-3 [5] DOI: 10.1063/1.529811 · Zbl 0769.60101 · doi:10.1063/1.529811 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.