With the development of quantum wireless networks, the practical application of quantum private query (QPQ) should conform to the features of quantum wireless networks to achieve any-to-any query, and QPQ requires a new query mechanism. We first propose a scheme for a network private query in a quantum wireless network with multiple third parties, in which any user can query any database with the assistance of the third parties, by measuring each of the distant nodes that initially share entanglement with each other. The required entanglement among these nodes is established by the third-party intermediate node equipped with GHZ generator using multi-qubit GHZ states. A bilayer network topology, as well as the corresponding private query protocol, ensures the rapid and secure private query. Under the protection of the multi-qubit GHZ state's quantum correlation, the privacy of Alice and Bob is protected from the third parties' fake entangled attack and external attack, and they cannot obtain the privacy of each other by taking quantum memory attack. The performance parameters of the proposed scheme are described based on the analysis of classical wireless communication cost and communication delay.
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