Controllable quantum private queries using an entangled Fibonacci-sequence spiral source

•Alice can easily control the size of a block by adjusting the parameter m rather than a high-dimension oracle.•The case of Alice knowing an exact multi-bit message can be realized deterministically.•Our protocol provides broad measures of protection against errors caused by the effect of noise.•Our protocol can greatly save both quantum and classical communication and exhibit some advantages in security.•Our protocol is scalable and flexible, and secure against quantum memory attacks by Alice.

By changing the initial values in entangled Fibonacci-sequence spiral sources in Simon et al.'s (2013) experimental setup [13], we propose a controllable quantum private query protocol. Moreover, our protocol achieves flexible key expansion and even exhibits secure advantages during communications because of the following observations. We observe the close relationships between Lucas numbers and the first kind of Chebyshev maps, and the Chebyshev maps and k-Chebyshev maps; by adjusting the parameter m in k-Chebyshev maps, Alice and Bob can obtain their expected values of the key blocks and database respectively.