Entropic characteristics of photon tomograms

We study the electromagnetic-field tomograms for classical and quantum states. We use the violation of the positivity of entropy for the photon-probability distributions for distinguishing the classical and quantum domains. We show that the photon-probability distribution expressed in terms of optical or symplectic tomograms of the photon quantum state must be a nonnegative function, which yields the nonnegative Shannon entropy. We also show that the optical tomogram of the photon classical state provides the expression for the Shannon entropy, which can be nonpositive.