  In view of the tomographic-probability representation of quantum states, we
reconsider the approach to quantumness tests of a single system developed in
[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.
