# Quantum Privacy Query Protocol Based on GHZ-like States
## 1 Introduction  
Traditional medical diagnosis is based on a physician's medical knowledge, clinical insight, and the ability to integrate and analyze available information. However, experienced doctors will inevitably make mistakes. With the rapid progress of computer and network technology, medical-assisted diagnosis systems have also received significant attention and development [1]. Online medical assistance systems utilize computer technology and artificial intelligence to provide medical advice, diagnosis, and treatment recommendations. These systems, which are usually delivered via the internet or mobile apps, can provide a variety of medical information and support to patients, physicians, and healthcare professionals. Patients can enter their symptoms online, and the system will provide initial medical advice to help them understand a possible disease or health problem. Patients are then given information about diseases, medications, treatments, and health advice to help them better understand and manage their health conditions. According to the literature [2], which combines decision tree and Oblivious Transfer (OT) technology to achieve two-way privacy protection in medical-assisted diagnosis systems, one researcher proposed a decision tree indexing protocol, which can efficiently digitize the decision tree information, thus facilitating the use of OT protocol to protect the client's privacy [3] and at the same time ensuring that the client can only obtain the query related information and not other additional information. However, the security field still faces severe challenges. As technology continues to advance, the rapid development of quantum computing capabilities has become a focus of widespread concern. The rise of this emerging technology has raised significant concerns about information security. The power of quantum computing promises to break some of the classical encryption algorithms currently considered secure, including those widely used in the classical Oblivious Transfer protocol [4]. However, quantum algorithms are becoming increasingly sophisticated, and the security of these schemes based on complicated mathematical assumptions deserves reconsideration. Fortunately, quantum cryptography and quantum mechanical principles can solvethe security problems of classical SPIR schemes [5]. The protocol that deals with these problems using quantum cryptography and quantum mechanics can be called quantum private query (QPQ [6; 7; 8]). Quantum private query is a privacy protection technology involving quantum computing, whose goal is to protect the security of users and databases. In 2008, [PERSON] et al. [9] proposed the first QPQ protocol (GLM), and then the security of the protocol is demonstrated through experiments [10]. The GLM protocol has a substantial improvement in safety, and the complexity required for computation and communication shows an exponential decrease. Nevertheless, the GLM protocol is no longer applicable when the database data increases substantially. To accommodate the large databases, [PERSON] et al. [11] proposed a QPQ protocol based on quantum key distribution (j-protocol). It is worth noting that in this protocol, the database knows all the keys while the user knows only part of the keys, so it is necessary to dilute the user's known key to almost 1 bit, and this dilution algorithm is called a post-processing algorithm [12]. To make the protocol more flexible, [PERSON] et al. [13] introduced a new parameter \(\theta\) in the j protocol to make it highly flexible. Quantum states in \(\{|0\rangle,|1\rangle,\cos\ \theta|0\rangle+\sin\ \theta|1\rangle,\sin\ \theta|0\rangle-\cos\ \theta|1\rangle\}\) are used in this protocol to realize a more flexible j protocol. Although the security and communication efficiency of the protocol can be changed by adjusting the value of the parameter \(\theta\), the quantum resources are not easy to prepare. In 2015, [PERSON] et al. [14] proposed another QPQ scheme using one quantum state.