Calculation of the Quantum Entanglement Measure of Bipartite States, Based on Relative Entropy, Using Genetic Algorithms

Quantum entanglement is an enigmatic and powerful property that has attracted much attention, since it provides new means of communication, such as quantum cryptography, quantum teleportation and superdense coding, and quantum computation. Therefore, the measure of entanglement of composite systems becomes crucial. For pure bipartite states the von Neumann entropy is a good measure and it is easily calculated; however, to quantify the entanglement of mixed states is a harder task. Some measures have been proposed, among them one based on relative entropy. This measure needs a minimization procedure. In this paper, we present an algorithm to calculate the quantum entanglement measure based on relative entropy, in which the required minimization procedure is done using a genetic algorithm. The main advantage of using a genetic algorithm is it is easier to implement than gradient methods are when the number of parameters is very large.