(1) Faculty of Physics, M.V. Lomonosov Moscow State University, Vorob’evy Gory, Moscow, 119992, Russia;(2) P.N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect, 53, Moscow, 119991, Russia
Abstract:
A linear map of qudit tomogram onto qubit tomogram (qubit portrait) is proposed as a characteristics of the qudit state. In view of the qubit-portrait method, the Bell inequalities for two qubits and two qutrits are discussed within the framework of the probability-representation of quantum mechanics. A semigroup of stochastic matrices is associated with tomographic-probability distributions of qubit and qutrit states. Bell-like inequalities are studied using the semigroup of stochastic matrices. The qudit-qubit map of tomographic probability distributions is discussed as an ansatz to provide a necessary condition for the separability of quantum states.