Qubit portrait of qudit states and Bell inequalities

Abstract

A linear map of qudit tomogram onto qubit tomogram (qubit portrait) is proposed as a characteristics of the qudit state. Using the qubit portrait method the Bell inequalities for two qubits and two qutrits are discussed in framework of probability representation of quantum mechanics. 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 ansatz to provide a necessary condition for separability of quantum states.