# Device Independent Quantum Private Query with Finite Number of Entangled Qubits

## TL;DR

This paper extends device-independent quantum private query protocols to finite qubit scenarios, linking sample size to success probability and providing a rigorous security analysis for practical implementation.

## Contribution

It upgrades existing protocols to finite qubits and establishes a connection between sample size and CHSH test success probability, with a detailed security analysis.

## Key findings

- Protocol successfully adapted for finite qubits
- Sample size directly influences CHSH test success probability
- Rigorous security proof provided for the finite case

## Abstract

In a recent work by Maitra et al. (Phys. Rev. A, 2017), it was shown that the existing Quantum Private Query (QPQ) protocols fail to maintain the database security if the entangled states shared between Alice and Bob are not of a certain form. So it is necessary to certify the states a priori. In this regard, the local CHSH test was proposed. However, the proposed scheme works perfectly for the asymptotic case when we have infinite number of qubits. In this brief report, we upgrade the protocol for finite number of qubits and connect the sample size to the success probability of CHSH test. We also perform a rigorous security analysis of the proposed protocol.