In this paper, we study the problem of quantitative group testing (QGT) and analyze the performance of three models: the noiseless model, the additive Gaussian noise model, and the noisy Z-channel model. For each model, we analyze two algorithmic approaches: a linear estimator based on correlation scores, and a least squares estimator (LSE). We derive upper bounds on the number of tests required for exact recovery with vanishing error probability, and complement these results with information-theoretic lower bounds. In the additive Gaussian noise setting, our lower and upper bounds match in order.

翻译：本文研究定量群测（QGT）问题，并分析三种模型的性能：无噪声模型、加性高斯噪声模型以及有噪Z信道模型。针对每种模型，我们探讨两种算法方法：基于相关性得分的线性估计器和最小二乘估计器（LSE）。我们推导出在误差概率趋近于零时实现精确恢复所需测试数量的上界，并借助信息论下界对这些结果进行补充。在加性高斯噪声场景下，我们的上界与下界在阶数上保持一致。