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  1. The inaccuracy principle.Hans Martens & Willem M. de Muynck - 1990 - Foundations of Physics 20 (4):357-380.
    The problem of joint measurement of incompatible observables is investigated. Measurements are represented by positive operator-valued measures. A quantitative notion of inaccuracy is defined. It is shown that within this framework joint inaccurate measurements are possible for arbitrary maximal projection-valued measures on finite-dimensional spaces. The accuracy of such measurements is limited, as is shown by an inaccuracy inequality we derive. This new type of uncertainty relation can be unambiguously interpreted as referring to measurement precision rather than preparative quality. Several recent (...)
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  • Reduction and Extremality of Finite Observables.Heinz-Jürgen Schmidt - 2019 - Foundations of Physics 49 (6):577-593.
    We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one observables and consider various constructions that reduce observables to simpler ones. However, these constructions do not suffice to generate all finite extremal observables, as we show by means of counter-examples.
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