We present the original semi-algebraic method for the effective computation of discord in the multi-qubit spin chain interacting with the impurity spin. We use the random mutations algorithm in a non-standard way: not for the minimization, but for the verification of inequalities. More specifically, we use it to check the constancy condition of the minimum of conditional entropy. After that, the discord can be calculated effectively by the algebraic procedures, and we construct the discord surface for different values of the structural parameter of the model.
The considered approach for the verification of inequalities by global optimization algorithms can be used in a wide variety of applications, especially, in the theory of quantum correlations, which contains a lot of definitions based on minimums and maximums.