Quantum Symmetric Private Information Retrieval with Secure Storage and Eavesdroppers

TL;DR

This paper introduces new classical and quantum schemes for symmetric private information retrieval that are secure against eavesdroppers and collusion, achieving optimal rates with innovative alignment techniques and quantum entanglement.

Contribution

First to study $X$-secure, $E$-eavesdropped, and $T$-colluding SPIR in both classical and quantum settings, developing novel schemes with optimal rates.

Findings

Classical scheme achieves rate $1 - \frac{X+\max(T,E)}{N}$.

Quantum scheme maintains super-dense coding gain, achieving rate $\min\left\{ 1, 2\left(1-\frac{X+\max(T,E)}{N}\right)\right\}.

First work to consider eavesdroppers in quantum PIR.

Abstract

We consider both the classical and quantum variations of $X$-secure, $E$-eavesdropped and $T$-colluding symmetric private information retrieval (SPIR). This is the first work to study SPIR with $X$-security in classical or quantum variations. We first develop a scheme for classical $X$-secure, $E$-eavesdropped and $T$-colluding SPIR (XSETSPIR) based on a modified version of cross subspace alignment (CSA), which achieves a rate of $R= 1 - \frac{X+\max(T,E)}{N}$. The modified scheme achieves the same rate as the scheme used for $X$-secure PIR with the extra benefit of symmetric privacy. Next, we extend this scheme to its quantum counterpart based on the $N$-sum box abstraction. This is the first work to consider the presence of eavesdroppers in quantum private information retrieval (QPIR). In the quantum variation, the eavesdroppers have better access to information over the quantum channel compared to the classical channel due to the over-the-air decodability. To that end, we develop another scheme specialized to combat eavesdroppers over quantum channels. The scheme proposed for $X$-secure, $E$-eavesdropped and $T$-colluding quantum SPIR (XSETQSPIR) in this work maintains the super-dense coding gain from the shared entanglement between the databases, i.e., achieves a rate of $R_Q = \min\left\{ 1, 2\left(1-\frac{X+\max(T,E)}{N}\right)\right\}$.