Tsallis relative α entropy of coherence dynamics in Grover′s search algorithm

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 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.

Coherence dynamics in quantum algorithm for linear systems of equations

“…It is found that the overall effect in Grover's search algorithm is that the l 1 norm of coherence is depleted during the quantum search process [68], and the complementarity relation between the success probability and coherence has been derived [69]. Following the idea in [68,69], coherence dynamics in Grover's search algorithm has been studied based on Tsallis relative α entropy [70]. Recently, Feng, Chen and Zhao have studied coherence and entanglement in Grover and HHL algorithm [71].…”