用神经网络证明：某些量子测量仅需1比特即可高精度模拟。
Neural Network Learning of One-Bit Protocols for Qubit Measurement Simulation
- 用神经网络学习1比特通信下的量子测量模拟策略
- 对对称测量（如正多面体）平均准确率接近完美
- 适用于信息完备的对称测量场景，尤其适合理论研究
通信复杂性为量化经典资源以复现量子统计提供了自然框架。在量子态制备与测量场景中，已有研究表明，两个经典比特足以精确模拟任意量子态和测量。然而，该结果不排除特定测量族可实现高精度的1比特经典近似。本文采用神经网络方法证明，对于特定测量族，单比特通信即可实现高平均精度。性能分析显示，具有均匀权重元素的对称测量（如构成正多面体的测量）特别适合此类简化通信。通过分析神经网络所学模式，我们推导出一种解析协议，对该类有限信息完备的对称配置极为准确，并在连续各向同性测量极限下趋于精确。
原文摘要 · Abstract (English)
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.
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