Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation

TL;DR

This paper analyzes how quantum coherence acts as a resource in the Deutsch-Jozsa algorithm and its variations, comparing quantum and classical success probabilities in decision problems.

Contribution

It applies a quantitative coherence theory to analyze the role of coherence in the Deutsch-Jozsa algorithm and introduces a variation with different error constraints.

Findings

Quantum coherence influences success probabilities in decision problems.

Quantum procedures outperform classical ones in specific probabilistic settings.

Coherence serves as a quantifiable resource in quantum decision algorithms.

Abstract

That superpositions of states can be useful for performing tasks in quantum systems has been known since the early days of quantum information, but only recently has quantitative theory of quantum coherence been proposed. Here we apply that theory to an analysis of the Deutsch-Jozsa algorithm, which depends on quantum coherence for its operation. The Deutsch-Jozsa algorithm solves a decision problem, and we focus on a probabilistic version of that problem, comparing probability of being correct for both classical and quantum procedures. In addition, we study a related decision problem in which the quantum procedure has one-sided error while the classical procedure has two-sided error. The role of coherence on the quantum success probabilities in both of these problems is examined.