发表机构
Fundació i2CAT, internet i innovació digital a Catalunya; Universitat Politècnica de Catalunya; Universitat Autònoma de Barcelona; Universität Siegen（加泰罗尼亚互联网与数字创新i2CAT基金会; 加泰罗尼亚理工大学; 巴塞罗那自治大学; 锡根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究量子比特测量模拟中受限测量族的单比特经典近似，用神经网络程序证明单比特对特定测量族可实现高平均精度，分析其性能并推导出对特定配置准确且在特定极限下精确的解析协议。
AI 中文摘要
通信复杂性为量化重现量子统计所需的经典资源提供了一个自然框架。在量子比特制备与测量场景中，已表明两个经典比特对于精确模拟任意量子比特态和任意量子测量是必要且充分的。然而，这一结果并不排除受限测量族可能允许精确的单比特经典近似的可能性。我们使用神经网络程序证明，对于特定测量族，单个比特可实现较高的平均精度。对我们的神经网络的性能分析表明，具有均匀加权元素的对称测量，例如那些形成正多面体的测量，特别适合这种受限通信。通过分析神经网络学习的模式，我们推导出一种解析协议，该协议对于有限信息完全对称配置极其准确，并且在连续各向同性测量的极限情况下变得精确。
英文摘要
Communication complexity provides a natural framework for quantifying the classical resources required to reproduce quantum statistics. In the qubit prepare-and-measure scenario, two classical bits have been shown to be necessary and sufficient to simulate arbitrary qubit states and arbi- trary quantum measurements exactly. However, this result does not exclude the possibility that restricted families of measurements may admit accurate 1-bit classical approximations. We use a neural network procedure to demonstrate that a single bit can achieve high average accuracy for specific measurement families. A performance analysis of our neural network reveals that symmet- ric measurements with uniformly weighted elements, such as those forming regular polyhedra, are particularly amenable to this restricted communication. By analyzing the patterns learned by the neural network, we derive an analytical protocol that is extremely accurate for finite information- ally complete symmetric configurations and becomes exact in the limit of a continuous isotropic measurement.
Comments9 pages with the main text and 9 pages with Appendix
