Coherence dynamics in Simon's quantum algorithm

TL;DR

This paper analyzes the coherence dynamics in Simon's quantum algorithm, revealing how coherence depends on system dimension and changes during the algorithm's execution.

Contribution

It introduces a coherence analysis based on Tsallis entropy and $l_{1,p}$ norm, providing new insights into coherence behavior in Simon's algorithm.

Findings

Coherence of both registers depends on the dimension N and increases with N.

The oracle operator O does not alter the coherence.

Coherence is produced when N>4 and depleted when N<4.

Abstract

Quantum coherence plays a pivotal role in quantum algorithms. We study the coherence dynamics of the evolved states in Simon's quantum algorithm based on Tsallis relative $\alpha$ entropy and $l_{1,p}$ norm. We prove that the coherences of the first register and the second register both rely on the dimension $N$ of the state spaces of the $n$ qubit systems, and increase with the increase of $N$. We show that the oracle operator $O$ does not change the coherence. Moreover, we study the coherence dynamics in the Simon's quantum algorithm and prove that in overall the coherence is in production when $N>4$ and in depletion when $N<4$.