Quantum private query protocol based on counterfactual quantum key distribution with noiseless attack

Most of the previous quantum private query protocols are based on the BB84 key distribution type and generally use a method that wastes most quantum resources to complete security detection. In order to save resources, this paper proposes a noiseless counterfactual quantum private query protocol with high efficiency. This protocol improves the counterfactual quantum key distribution protocol proposed by Rao and Srikanth (Phys Rev A 104:022424, 2021. https://doi.org/10.1103/PhysRevA.104.022424). The communicating parties randomly select quantum bits with probability f to perform flipping to complete the quantum private query. The detector at the sending end receives the counterfactual bit, which we use for security detection; the detector at the receiving end is called a non-counterfactual bit, which is combined with random bit flipping to realize key transmission, followed by traditional post-processing and private query. Finally, when \(f=0.5\), the response probability (keys rate) of the non-counterfactual detector at the receiving end can reach a minimum value of 0.5.