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.
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Chernega, V.N., Man’ko, V.I. Qubit portrait of qudit states and Bell inequalities. J Russ Laser Res 28, 103–124 (2007). https://doi.org/10.1007/s10946-007-0005-8
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DOI: https://doi.org/10.1007/s10946-007-0005-8