# Capacity of Quantum Private Information Retrieval with Multiple Servers

## TL;DR

This paper investigates the maximum efficiency of quantum private information retrieval with multiple servers, demonstrating that the capacity can reach 1 under certain conditions and surpasses classical methods.

## Contribution

It proves the capacity of multi-server QPIR is 1 with entanglement, constructs a rate-one protocol with two servers, and establishes a strong converse bound without secrecy constraints.

## Key findings

- Capacity of QPIR with entanglement is 1 regardless of servers and files.
- Constructed a rate-one protocol with two servers.
- Proved the capacity of multi-round QPIR is 1.

## Abstract

We study the capacity of quantum private information retrieval (QPIR) with multiple servers. In the QPIR problem with multiple servers, a user retrieves a classical file by downloading quantum systems from multiple servers each of which contains the copy of a classical file set while the identity of the downloaded file is not leaked to each server. The QPIR capacity is defined as the maximum rate of the file size over the whole dimension of the downloaded quantum systems. When the servers are assumed to share prior entanglement, we prove that the QPIR capacity with multiple servers is 1 regardless of the number of servers and files. We construct a rate-one protocol only with two servers. This capacity-achieving protocol outperforms its classical counterpart in the sense of capacity, server secrecy, and upload cost. The strong converse bound is derived concisely without using any secrecy condition. We also prove that the capacity of multi-round QPIR is 1.