Degeneration of the Grover search algorithm with depolarization in the oracle-box wires

Abstract

Grover’s search algorithm and similar techniques are widely used in quantum information science. Communication lines with the so-called oracle are one of inevitable vulnerabilities of quantum search. The impact of localized dephasing and amplitude damping on Grover’s algorithm had already been discussed in recent literature. In this paper, we study the influence of depolarization in the oracle-box wires on the search process. It is shown that even low level of noise is sufficient to degenerate Grover’s algorithm. Complementarity relations between the relative entropy of coherence and the success probability in the presence of depolarization are studied as well.