Static and dynamic coherence fraction in the Bernstein-Vazirani algorithm

TL;DR

This paper investigates how the coherence fraction of the initial quantum state influences the success probability of the Bernstein-Vazirani algorithm, revealing that coherence fraction alone determines the algorithm's efficiency.

Contribution

It establishes a direct link between the coherence fraction and the success probability of the Bernstein-Vazirani algorithm, highlighting the importance of coherence in quantum computational performance.

Findings

Success probability depends solely on the coherence fraction of the initial state.

Coherence fraction dynamics relate to the algorithm's efficiency.

Quantum coherence fraction influences the effectiveness of quantum algorithms.

Abstract

Quantum entanglement and coherence are crucial resources in quantum information theory. In some scenarios, however, it is not necessary to directly estimate entanglement or coherence measures to quantify the capabilities of a state in quantum information processing. Instead, fully entangled fraction and coherence fraction are two alternatives for entanglement and coherence in specific quantum tasks. Here, we establish a link between the coherence fraction and the Bernstein-Vazirani algorithm, which has several potential applications including cryptography and database search. We show that the success probability of the generalized Bernstein-Vazirani algorithm depends only on the coherence fraction of the initial state rather than its entanglement or coherence. Moreover, we discuss the coherence fraction dynamics and establish a relation between the operator's coherence fraction and the algorithm's success probability. Our findings highlight how quantum coherence fraction influences the efficiency of quantum algorithms.