Effects of initial states on the quantum correlations in the generalized Grover search algorithm* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11975132 and 61772295), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019YQ01), and Shandong Province Higher Educational Science and Technology Program, China (Grant No. J18KZ012).

Abstract

We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation. Using a set of suitable bases, we construct the reduced density matrix and give the numerical expression of correlations relating to the iterations. For different initial states, we obtain the concurrence and quantum discord compared with the success probability in the algorithm. The results show that the initial states affect the correlations and the limit point of the correlations in the searching process. However, the initial states do not influence the whole cyclical trend.