Coherence depletion in the Grover quantum search algorithm

TL;DR

This paper explores how quantum coherence depletion affects the success probability of Grover's quantum search algorithm, revealing that coherence measures are directly related to search performance, unlike other quantum correlations.

Contribution

It demonstrates the specific role of quantum coherence depletion in Grover's algorithm and introduces the cost performance metric to quantify this relationship.

Findings

Success probability depends on quantum coherence depletion.

Quantum coherence measures correlate with search success, unlike other quantum correlations.

QCD increases with the required measurement time in generalized Grover algorithms.

Abstract

We investigate the role of quantum coherence depletion (QCD) in Grover search algorithm (GA) by using several typical measures of quantum coherence and quantum correlations. By using the relative entropy of coherence measure ($\mathcal{C}_r$), we show that the success probability depends on the QCD. The same phenomenon is also found by using the $l_1$ norm of coherence measure ($\mathcal{C}_{l_1}$). In the limit case, the cost performance is defined to characterize the behavior about QCD in enhancing the success probability of GA, which is only related to the number of searcher items and the scale of database, no matter using $\mathcal{C}_r$ or $\mathcal{C}_{l_1}$. In generalized Grover search algorithm (GGA), the QCD for a class of states increases with the required optimal measurement time. In comparison, the quantification of other quantum correlations in GA, such as pairwise entanglement, multipartite entanglement, pairwise discord and genuine multipartite discord, cannot be directly related to the success probability or the optimal measurement time. Additionally, we do not detect pairwise nonlocality or genuine tripartite nonlocality in GA since Clauser-Horne-Shimony-Holt inequality and Svetlichny's inequality are not violated.