Tutorial Lectures on Quantum Theory of Measurement

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 finite-size 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.