Quantum Correlation of Laser Entangled Photons Calculated Via Event-Based Method by Using Matlab Simulation

Abstract

Quantum correlations between particles are usually formulated by assuming the persistence of an entangled state after the particles have separated. When entanglement is present, Bell‘s Inequalities are violated but when entanglement is destroyed, Bell‘s inequalities are satisfied. The aim of this work is to build computer program using Matlab software to simulate Ekert protocol of quantum cryptography by implement event-based simulation method. And by used two types of probabilistic polarizing beam splitter. Since we used the argument of Malus intensity law to represent the quantum probability amplitude for each single photon in type1 and the Hadamard transformation of single photon to represent quantum probability amplitude for each single photon in type2. The program calculated the quantum correlation of each two polarized entangled photons as a value of Bell inequality (S) . The obtained results of (S) value after implemented suitable time tag model was in average S = 2.6 for type1, and S = 2.7 for type2. And this results investigated strong quantum correlation, and very agreement with that result of maximum correlation expected by quantum mechanics theory calculated for polarized entangled photons (S =2.83). After running the simulation program of Ekert protocol the results of established secret key between two legitimate users and the variation of (S) value showed very good ability of program for detecting eavesdropper, that by an obvious decrease in (S) value. When eavesdropper was present the value of (S) decreased to S = -0.29 and S = 0.19for type1 and type2 respectively.