Practical quantum private query of blocks based on unbalanced-state Bennett-Brassard-1984 quantum-key-distribution protocol

Until now, the only kind of practical quantum private query (QPQ), quantum-key-distribution (QKD)-based QPQ, focuses on the retrieval of a single bit. In fact, meaningful message is generally composed of multiple adjacent bits (i.e., a multi-bit block). To obtain a message a(1)a(2) ..a(l) from database, the user Alice has to query l times to get each a(i). In this condition, the server Bob could gain Alice's privacy once he obtains the address she queried in any of the l queries, since each a(i) contributes to the message Alice retrieves. Apparently, the longer the retrieved message is, the worse the user privacy becomes. To solve this problem, via an unbalanced-state technique and based on a variant of multi-level BB84 protocol, we present a protocol for QPQ of blocks, which allows the user to retrieve a multi-bit block from database in one query. Our protocol is somewhat like the high-dimension version of the first QKD-based QPQ protocol proposed by Jacobi et al., but some nontrivial modifications are necessary.