Heisenberg's uncertainty principle is usually taken to express a limitation of operational
possibilities imposed by quantum mechanics. Here we demonstrate that the full content of …

Quantum harmonic analysis on phase space is shown to be linked with localization
operators. The convolution between operators and the convolution between a function and …

On a locally compact group we introduce covariant quantization schemes and analogs of
phase space representations as well as mixed-state localization operators. These …

We generalize the concept of the weak value of a quantum observable to cover arbitrary real
positive operator measures. We show that the definition is operationally meaningful in the …

We study mixed-state localization operators from the perspective of Werner's operator
convolutions which allows us to extend known results from the rank-one case to trace class …

Heisenberg's uncertainty principle has recently led to general measurement uncertainty
relations for quantum systems: incompatible observables can be measured jointly or in …

We discuss symmetric quantum measurements and the associated covariant observables
modelled, respectively, as instruments and positive-operator-valued measures. The …

which together comprise the full content of the uncertainty: this relation can be read as
describing a trade-off (a) between the widths of the probability distributions of position and …

Positive operator measures (with values in the space of bounded operators on a Hilbert
space) and their generalizations, mainly positive sesquilinear form measures, are …

Joint approximate measurement schemes of position and momentum provide us with a
means of inferring pieces of complementary information if we allow for the irreducible noise …