Abstract
Different kinds of entropy associated with probability distribution functions characterizing the system state in classical and quantum domains are reviewed. Shannon entropy and Rényi entropy are discussed. The notion of tomographic entropy determined by the probability distribution in the phase space of the classical system and by the density operator of the quantum system is considered. Inequalities for the tomographic entropies in classical and quantum domains are studied, and a difference in the form of these inequalities in corresponding domains is suggested as a test to clarify the classicality and quantumness of the system state in quantum optics experiments. A new bound for tomographic entropy (ln πe)Φ(θ) depending on the local oscillator phase difference in homodyne photon detection experiments is discussed.
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