Partial order of quantum effects
- 1 April 1995
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 36 (4) , 1673-1680
- https://doi.org/10.1063/1.531079
Abstract
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.Keywords
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