Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm

TL;DR

This paper investigates how the Tsallis relative alpha entropy of coherence evolves during Grover's search algorithm, revealing its relationship with success probability, entanglement, and database size.

Contribution

It provides new theoretical insights into the dynamics of quantum coherence and its complementarity with success probability in Grover's algorithm.

Findings

Coherence decreases as success probability increases.

Derived complementarity relations between coherence and success probability.

Showed operator coherence depends on database size, success probability, and target states.

Abstract

Quantum coherence plays a central role in Grover's search algorithm. We study the Tsallis relative $\alpha$ entropy of coherence dynamics of the evolved state in Grover's search algorithm. We prove that the Tsallis relative $\alpha$ entropy of coherence decreases with the increase of the success probability, and derive the complementarity relations between the coherence and the success probability. We show that the operator coherence of the first $H^{\otimes n}$ relies on the size of the database $N$, the success probability and the target states. Moreover, we illustrate the relationships between coherence and entanglement of the superposition state of targets, as well as the production and deletion of coherence in Grover iterations.