6 research outputs found
Quantum Private Information Retrieval with Sublinear Communication Complexity
This note presents a quantum protocol for private information retrieval, in
the single-server case and with information-theoretical privacy, that has
O(\sqrt{n})-qubit communication complexity, where n denotes the size of the
database. In comparison, it is known that any classical protocol must use
\Omega(n) bits of communication in this setting.Comment: 4 page
On Quantum Advantage in Information Theoretic Single-Server PIR
In (single-server) Private Information Retrieval (PIR), a server holds a
large database of size , and a client holds an index and
wishes to retrieve without revealing to the server. It is well
known that information theoretic privacy even against an `honest but curious'
server requires communication complexity. This is true even if
quantum communication is allowed and is due to the ability of such an
adversarial server to execute the protocol on a superposition of databases
instead of on a specific database (`input purification attack'). Nevertheless,
there have been some proposals of protocols that achieve sub-linear
communication and appear to provide some notion of privacy. Most notably, a
protocol due to Le Gall (ToC 2012) with communication complexity ,
and a protocol by Kerenidis et al. (QIC 2016) with communication complexity
, and shared entanglement.
We show that, in a sense, input purification is the only potent adversarial
strategy, and protocols such as the two protocols above are secure in a
restricted variant of the quantum honest but curious (a.k.a specious) model.
More explicitly, we propose a restricted privacy notion called \emph{anchored
privacy}, where the adversary is forced to execute on a classical database
(i.e. the execution is anchored to a classical database). We show that for
measurement-free protocols, anchored security against honest adversarial
servers implies anchored privacy even against specious adversaries.
Finally, we prove that even with (unlimited) pre-shared entanglement it is
impossible to achieve security in the standard specious model with sub-linear
communication, thus further substantiating the necessity of our relaxation.
This lower bound may be of independent interest (in particular recalling that
PIR is a special case of Fully Homomorphic Encryption)