Quantum Private Information Retrieval has Linear Communication Complexity

• Published in: Journal of cryptology Vol. 28; no. 1; pp. 161 - 175
• Main Authors: Baumeler, Ämin, Broadbent, Anne
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-01-2015; Springer Nature B.V
• Subjects: Coding and Information Theory; Combinatorics; Communication; Communications Engineering; Complexity; Computational Mathematics and Numerical Analysis; Computer Science; Cryptography; Information retrieval; Lower bounds; Networks; Privacy; Probability Theory and Stochastic Processes; Qubits (quantum computing); Private information retrieval; Specious adversaries; Quantum semi-honest; Quantum cryptography
• ISSN: 0933-2790; 1432-1378
• DOI: 10.1007/s00145-014-9180-2

In private information retrieval (PIR), a client queries an
n
-bit database in order to retrieve an entry of her choice, while maintaining privacy of her query value. Chor et al. [J ACM 45(6):965–981,
1998
] showed that, in the information-theoretical setting, a linear amount of communication is required for classical PIR protocols (thus the trivial protocol is optimal). This linear lower bound was shown by Nayak [FOCS 1999, pp. 369–376,
1999
] to hold also in the quantum setting. Here, we extend Nayak’s result by considering approximate privacy, and requiring security only against
specious
adversaries, which are, in analogy to classical honest-but-curious adversaries, the weakest reasonable quantum adversaries. We show that, even in this weakened scenario, quantum private information retrieval (QPIR) requires 
n
qubits of communication. From this follows that Le Gall’s recent QPIR protocol with sublinear communication complexity [Theory Comput. 8(1):369–374,
2012
] is not information-theoretically private, against the weakest reasonable cryptographic adversary.