On the role of dealing with quantum coherence in amplitude amplification

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.

15 pages, 2 figures. Major revision in v2. The bibliography is extended and updated. To appear in Quantum Information Processing

References in corpus (7)

• The Fidelity and Trace Norm Distances for Quantifying Coherence
• Maximal Coherence and the Resource Theory of Purity
• Quantum uncertainty relation using coherence
• Grover's Quantum Search Algorithm for an Arbitrary Initial Mixed State
• Uncertainty Relations for Quantum Coherence
• Estimation on geometric measure of quantum coherence
• Uncertainty relations for quantum coherence with respect to mutually unbiased bases

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• Quantum search degeneration under amplitude noise in queries to the oracle
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