We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
42/2024
Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm
Linlin Ye, Zhaoqi Wu and Shao-Ming Fei
Abstract
Quantum coherence plays a central role in the 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 for $\alpha\in(1,2]$. Moreover, we illustrate the relations between the coherence and the entanglement of the superposition state of targets, as well as the coherence producing and deleting in the Grover iterations.
