Quantum private information retrieval (QPIR) for quantum messages is the protocol in which a user retrieves one of the multiple quantum states from one or multiple servers without revealing which state is retrieved. We consider QPIR in two different settings: the blind setting, in which the servers contain one copy of the message states, and the visible setting, in which the servers contain the description of the message states. One trivial solution in both settings is downloading all states from the servers and the main goal of this paper is to find more efficient QPIR protocols. First, we prove that the trivial solution is optimal for one-server QPIR in the blind setting. In one-round protocols, the same optimality holds even in the visible setting. On the other hand, when the user and the server share entanglement, we prove that there exists an efficient one-server QPIR protocol in the blind setting. Furthermore, in the visible setting, we prove that it is possible to construct symmetric QPIR protocols in which the user obtains no information of the non-targeted messages. We construct three two-server symmetric QPIR protocols for pure states. Note that symmetric classical PIR is impossible without shared randomness unknown to the user.

中文翻译：

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量子消息的量子私有信息检索

用于量子消息的量子专用信息检索（QPIR）是一种协议，在该协议中，用户从一个或多个服务器中检索多个量子状态之一，而不显示要检索的状态。我们在两种不同的设置中考虑QPIR：盲设置（其中服务器包含消息状态的一个副本）和可见设置（服务器中包含消息状态的描述）。在这两种设置中，一个简单的解决方案是从服务器下载所有状态，并且本文的主要目标是找到更有效的QPIR协议。首先，我们证明了平凡的解决方案对于盲环境中的单服务器QPIR是最佳的。在单轮协议中，即使在可见环境下也保持相同的最优性。另一方面，当用户和服务器共享纠缠时，我们证明在盲环境中存在一种有效的单服务器QPIR协议。此外，在可见环境中，我们证明可以构造对称的QPIR协议，其中用户不获取非目标消息的信息。我们为纯状态构造了三个两服务器对称QPIR协议。请注意，如果没有用户未知的共享随机性，则对称经典PIR是不可能的。