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Quantum observations (Tutorial lectures) Vladimír Bužek Research Center for Quantum Information, Slovak Academy of Sciences, Bratislava In my tutorial lectures I will briefly outline some epistemological as well as operational problems associated with the quantum theory of measurement. I will address several topics including: Basic concepts - Why quantum measurements are so much different from classical observations? Maximum entropy principle - I will discuss how states of quantum systems can be reconstructed from incomplete experimental data when meanvalues of a limited number of the system observables are available from a measurement. Quantum “clickology” - I will show how information can be extracted from finitesize ensembles of identically prepared quantum systems. I will discuss the role of resources available in measurement. In particular, I will present quantum version of the Bayesian inference method. Recycling of quantum information - I will address a question whether one can extract some useful information from a quantum system that has already been measured. Reconstruction of quantum channels - I will also show how quantum channels can be reconstructed from incomplete experimental data. Compression of quantum information – I will analyse how classical information can be efficiently compressed and encoded into quantum systems.