Proposal for Dimensionality Testing in Quantum Private Query

TL;DR

This paper highlights the importance of dimensionality testing in quantum private query protocols to prevent security loopholes and proposes a CHSH-like game-based method for effective testing of quantum state dimensions.

Contribution

It introduces a novel dimensionality testing method using a CHSH-like game to ensure security in quantum private query protocols.

Findings

Changing quantum state dimensions can give unfair advantages in protocols.

The proposed CHSH-like game effectively detects product states vulnerable to attacks.

Removing dimension assumptions can compromise protocol security.

Abstract

Recently, dimensionality testing of a quantum state has received extensive attention (Ac{\'i}n et al. Phys. Rev. Letts. 2006, Scarani et al. Phys. Rev. Letts. 2006). Security proofs of existing quantum information processing protocols rely on the assumption about the dimension of quantum states in which logical bits are encoded. However, removing such assumption may cause security loophole. In the present paper, we show that this is indeed the case. We choose two players' quantum private query protocol by Yang et al. (Quant. Inf. Process. 2014) as an example and show how one player can gain an unfair advantage by changing the dimension of subsystem of a shared quantum system. To resist such attack we propose dimensionality testing in a different way. Our proposal is based on CHSH like game. As we exploit CHSH like game, it can be used to test if the states are product states for which the protocol becomes completely vulnerable.