The generation and verification of quantum states are fundamental tasks for quantum information processing that have recently been investigated by Irani, Natarajan, Nirkhe, Rao and Yuen [CCC 2022] and Rosenthal and Yuen [ITCS 2022] under the term \emph{state synthesis}. This paper studies this concept from the viewpoint of quantum distributed computing, and especially distributed quantum Merlin-Arthur (dQMA) protocols. We first introduce a novel task, on a line, called state generation with distributed inputs (SGDI). In this task, the goal is to generate the quantum state $U\ket{\psi}$ at the rightmost node of the line, where $\ket{\psi}$ is a quantum state given at the leftmost node and $U$ is a unitary matrix whose description is distributed over the nodes of the line. We give a dQMA protocol for SGDI and utilize this protocol to construct a dQMA protocol for the Set Equality problem studied by Naor, Parter and Yogev [SODA 2020]. Our second contribution is a technique, based on a recent work by Zhu and Hayashi [Physical Review A, 2019], to create EPR-pairs between adjacent nodes of a network without quantum communication. As an application of this technique, we prove a general result showing how to convert any dQMA protocol on an arbitrary network into another dQMA protocol where the verification stage does not require any quantum communication.
翻译:量子国家的生成和核查是量子信息处理的基本任务,伊朗、纳塔拉扬、尼尔凯、拉奥和尤恩(CC CCC 2022)以及罗森塔尔和尤恩(ITts 2022)最近对量子分布计算,特别是分布的Merlin-Arthur(dQMA)协议,从量子分布计算的角度研究这一概念。我们首先在一条线上引入了一个新的任务,称为“州生成并分配投入(SGDI) ” 。在这项任务中,我们的目标是在线的最右节点产生量子状态$Ukets@psi},在左节点和Yuen[ITS 2022] 中,美元是一个量子状态,在左节点和美元是一个单一矩阵,其描述分布在线的节点上。我们给SSGDI(dQMA)一个量子协议,并使用这个协议来为Naor、Parter和Yogev(SODO)所研究的SQMA协议。我们的第二项贡献是一种技术,基于最近的一个通信阶段, 而不是直径核查网络, 需要另一个技术。