Abstract
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.
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