Static and Dynamic Coherence Fraction in the Bernstein‐Vazirani Algorithm

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, a link is established between the coherence fraction and the Bernstein–Vazirani algorithm, which has several potential applications including cryptography and database search. It is showed 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, the coherence fraction dynamics are discussed and a relation is established between the operator's coherence fraction and the algorithm's success probability. These findings highlight how quantum coherence fraction influences the efficiency of quantum algorithms.