Demonstration of the violation of bell inequality in quantum key distribution

Today, the data privacy has become very important. Quantum Key Distribution (QKD) system is developed in this area. QKD, coding technique with single-use method of encoding used keys (information and messages) security guarantees. The system is based on Quantum Mechanics (The Certainty Principle). However, in some cases for quantum communication, QKD are limited. In determining this limit Bell Inequality (CHSH Inequality, 1969) is used. Bell inequality shows a violation of Quantum Key Distribution. In this study, using the program of Matematica, QKD through bilateral quantum system (system with two qubits) has been investigating the leak case and the violations. We showed leakage and violations in these figures via the calculations results in Matematica program.