Ibort Latre, Luis AlbertoMan'ko, V. I.Marmo, G.Simoni, A.Ventriglia, F.2010-06-072010-06-072010-06-07Physics Letters A, 2010, vol. 374, n. 26, p. 2614-26170375-9601http://hdl.handle.net/10016/86914 pages, no figures.-- PACS codes: 03.65 Sq; 03.65.Wj.-- ArXiv pre-print available at: http://arxiv.org/abs/1004.0102We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics.application/pdfeng© ElsevierQuantum tomogramsSymplectic tomogramsProbability measuresWeyl-Heisenberg groupresearch articleMatemáticas10.1016/j.physleta.2010.04.056open access