Complete Bell tests for qubits-qudits systems

Bell inequalities give the basic tool to distinguish whether a general quantum system can be described by a local and realistic theory (LRT). Namely, they set an upper bound on a function (Bell function) that must hold when considering LRTs and can be violated otherwise. In 1995, R. Horodecki, P. Horodecki and M. Horodecki derived an analytical expression for the maximal value of the Bell function for qubit-qubit systems, i.e. the necessary and sufficient condition for any qubit-qubit system to be described by LRTs. In this work we extend this result to qubit-qudit systems and give the necessary and sufficient for any qubit-qudit system to be described by LRTs.