On entropy and information of quantum states

Shannon entropy and information are applied to study the properties of quantum states of a system in the probability representation of quantum mechanics. Examples of spin states and mixed Gaussian states of the two-mode system are considered. The relationship between the new entropy and the von Neumann entropy is reviewed. Two tomographic maps are considered within the framework of the star-product quantization. The explicit expression of tomographic entropy associated with photon-number tomogram of the two-mode state of photons is obtained in terms of Hermite polynomials of four variables. Based on a contribution to the International Conference “New Trends in Quantum Mechanics. Fundamental Aspects and Applications” (Palermo, Italy, November 2005).