玻色子和费米子高斯态的最优层析成像
Optimal tomography of bosonic and fermionic Gaussian states
浏览论文内容
中文总结 AI 辅助
研究玻色子和费米子高斯态的样本复杂度问题，利用高斯酉群表示理论及随机纯化通道推广，得出无论态的类型和能量限制，均可通过与模式数成二次方比例的副本数来学习这些态的结论。
中文摘要 AI 辅助
样本复杂度是学习量子态准确经典描述所需的最小副本数。玻色子和费米子高斯量子态在量子科学技术中起着关键作用。尽管其很重要，但样本复杂度尚未完全确定。我们解决了这个开放问题，表明无论态是纯态还是混合态，也与态的任何能量限制无关，玻色子和费米子高斯态都可以用与模式数成二次方比例的副本数来学习。我们通过使用高斯酉群的表示理论以及提出随机纯化通道在此设置及其他情况下的推广来得出这些结果。
英文摘要
The sample complexity is the minimum number of copies required to learn an accurate classical description of a quantum state. Bosonic and fermionic Gaussian quantum states are families of quantum states that play a key role in quantum science and technology, from quantum optics and many-body physics to quantum chemistry, quantum computing, and quantum information theory. Despite their importance, their sample complexity had not been fully determined. We settle this open problem and show that both bosonic and fermionic Gaussian states can be learned using a number of copies that scales quadratically in the number of modes, regardless of whether the state is pure or mixed, and independently of any energy bound on the state. We derive these results by using the representation theory of Gaussian unitaries and by putting forth a generalization of the random purification channel to this setting and beyond.
