# On the role of dealing with quantum coherence in amplitude amplification

## TL;DR

This paper explores how quantum coherence affects the success probability of amplitude amplification, analyzing trade-offs and complementarity relations using different coherence measures in various quantum scenarios.

## Contribution

It introduces a detailed analysis of the relationship between quantum coherence measures and amplitude amplification success, highlighting trade-offs and complementarity relations.

## Key findings

- Quantum coherence measures relate to success probability in amplitude amplification.
- Trade-off relations between coherence and success probability are established.
- Complementarity relations are illustrated with model scenarios.

## Abstract

Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the rotation operations and replacing the intermediate Hadamard transform with arbitrary unitary one. In addition, arbitrary initial distribution of the amplitudes may be prepared. We examine trade-off relations between measures of quantum coherence and the success probability in amplitude amplification processes. As measures of coherence, the geometric coherence and the relative entropy of coherence are considered. In terms of the relative entropy of coherence, complementarity relations with the success probability seem to be the most expository. The general relations presented are illustrated within several model scenarios of amplitude amplification processes.