Quantum Fourier transform and tomographic Rényi entropic inequalities

We show that the Rényi entropy associated with spin tomograms of quantum states satisfies new inequalities that depend on the quantum Fourier transform. We obtain the limiting inequality for the von Neumann entropy of quantum spin states and a new kind of entropy associated with the quantum Fourier transform. We consider possible connections with subadditivity and strong subadditivity conditions for tomographic entropies and von Neumann entropies.