On the noise-resolution duality, Heisenberg uncertainty and Shannon's information

Several variations of the Heisenberg uncertainty inequality are derived on the basis of `noise-resolution duality' recently proposed by us. The same approach leads to a related inequality that provides an upper limit for the information capacity of imaging systems in terms of the number of imaging quanta (particles) used in the experiment. These results are useful in the context of biomedical imaging constrained by the radiation dose delivered to the sample, or in imaging (e.g., astronomical) problems under low light conditions.