The contextuality and noncontextuality notions are considered in framework of probability representation of quantum states. Example of qutrit states and violation of the noncontextuality inequalities are presented by using the spin tomogram and tomographic symbols of the observables.
In view of the tomographic-probability representation of quantum states, we reconsider the approach to quantumness tests of a single system developed by Alicki and Van Ryn (2008 J. Phys. A: Math. Theor. 41 062001). For qubits we introduce a general family of quantumness witnesses, which are operators depending on an extra parameter. Spin tomogram and dual-spin tomographic symbols are used to study qubit examples and the test inequalities which are shown to satisfy simple relations within the framework of the standard probability theory.
A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the state tomograms which are considered either as a set of the probability distributions of random variables depending on extra parameters or as a single joint probability distribution of these random variables and random parameters with specific properties of the marginals. Examples of optical tomograms of photon states, symplectic tomograms, and unitary spin tomograms of qudits are given. A new universal integral inequality for generic wave function is obtained on the base of tomographic entropic uncertainty relations.