Correlations in Grover search

TL;DR

This paper investigates various quantum and classical correlations during Grover's search algorithm, revealing that different correlations behave distinctly and all vanish at the search's conclusion, highlighting their roles in quantum computation.

Contribution

It provides a comprehensive analysis of multiple correlations in Grover's search, including quantum discord and classical correlation, which had not been thoroughly examined before.

Findings

Quantum discord, classical correlation, and mutual information behave similarly during the search.

Concurrence differs in behavior from other correlations.

All correlations vanish at the end of the search, indicating their role in the process.

Abstract

Grover search is a well-known quantum algorithm that outperforms any classical search algorithm. It is known that quantum correlations such as entanglement are necessary for the power of quantum computation. But entanglement is not the only kind of quantum correlations. Other quantum correlations such as quantum discord are also useful to capture some aspects of the nonclassical correlation. We investigate several kinds of correlations including both quantum and classical in the whole process of Grover search algorithm. These correlations are the concurrence, entanglement of formation, quantum discord, classical correlation and mutual information. The behaviors of quantum discord, classical correlation and mutual information are almost the same while the concurrence is different. When the search is over, all kinds of correlations are zero, we argue that this is necessary for the final step in the search.