发表机构
University of Cambridge; Carnegie Mellon University; University of Washington（剑桥大学; 卡内基梅隆大学; 华盛顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究量子可分解随机编码与量子私有同时消息协议的联系，揭示预共享纠缠量对量子编码大小和通信复杂度的核心影响，并给出上下界。
AI 中文摘要
我们研究了量子可分解随机编码（QDRE）的复杂度。我们在QDRE模型与量子私有同时消息协议（QPSM）的通信复杂度模型之间建立了双向联系，其中经典通信是免费的，而量子通信是主要复杂度度量。我们展示了以下上界和下界。（1）对于每个将$n$个量子比特映射到$m$个量子比特的量子信道，我们给出一个量子通信量为$m$的QPSM协议，使用指数级预共享纠缠。特别地，常量输出信道具有$O(1)$量子通信，而经典输出信道不需要量子通信。（2）使用$O(n)$预共享纠缠，每个单量子比特输出信道都有一个$O(n)$量子通信的QPSM协议。相反，存在一个信道和常数$c>0$，使得任何具有至多$cn$预共享纠缠的协议需要$\Omega(n)$量子通信。（3）相比之下，我们识别了一类结构化量子信道，即Clifford诱导信道，对于这些信道存在QPSM协议，具有$O(n)$预共享纠缠量子比特和仅$O(1)$量子通信复杂度。通过我们的联系，我们获得了QDRE量子编码大小的类似上界和下界。我们的结果表明，预共享纠缠的量在量子编码大小和量子通信复杂度中起着核心作用。
英文摘要
We study the complexity of quantum decomposable randomized encodings (QDRE). We establish a bi-directional connection between the QDRE model and the communication complexity model of quantum private simultaneous message protocols (QPSM), where classical communication is free, and quantum communication is the primary complexity measure. We show the following upper and lower bounds. (1) For every quantum channel mapping $n$ to $m$ qubits, we give a QPSM protocol with quantum communication $m$, using exponential pre-shared entanglement. In particular, constant-output channels have $O(1)$ quantum communication, and classical-output channels require no quantum communication. (2) With $O(n)$ pre-shared entanglement, every one-qubit-output channel has an $O(n)$-quantum-communication QPSM protocol. Conversely, there exists a channel and a constant $c>0$ for which any protocol with at most $cn$ pre-shared entanglement requires $Ω(n)$ quantum communication. (3) In contrast, we identify a structured class of quantum channels, Clifford-induced channels, for which there exist QPSM protocols with $O(n)$ pre-shared entangled qubits and only $O(1)$ quantum communication complexity. Through our connection, we obtain analogous upper and lower bounds on the quantum encoding size of QDRE. Our results show that the amount of pre-shared entanglement plays a central role in quantum encoding size and quantum communication complexity.
