发表机构
A*STAR Quantum Innovation Centre(Q.InC), Agency for Science, Technology and Research(A*STAR); Centre for Quantum Software and Information, University of Technology Sydney; Department of Quantum Science and Technology, Research School of Physics, The Australian National University; Centre for Quantum Technologies, National University of Singapore; Q-CTRL（A*STAR量子创新中心; 悉尼科技大学量子软件与信息研究中心; 澳大利亚国立大学物理研究学院量子科学与技术系; 新加坡国立大学量子技术中心; Q-CTRL）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明，在固定且无纠缠的单模玻色子系统中，利用压缩真空探针扩展可访问傅里叶带宽，可在学习随机位移分布时实现指数级样本复杂度降低，确立傅里叶带宽为量子增强学习的独立资源。
AI 中文摘要
量子资源可以显著减少学习物理系统所需的数据，在多项量子学习任务中，样本复杂度的指数级改进已得到证实。然而，这些优势通常依赖于随问题复杂度扩展的量子资源，尤其是系统维度的增加或纠缠。这引出了一个基本问题：在固定且无纠缠的量子系统中，能否出现指数级的量子学习优势？在本文中，我们通过考虑学习一个未知的随机位移分布来回答这个问题，该分布的复杂度并非由物理系统的维度决定，而是由其特征的傅里叶分辨率决定。我们证明，真空探针的量子极限噪声会逐渐掩盖高频特征，导致样本复杂度呈指数增长。我们为任意经典态探针建立了信息论下界，并证明压缩态通过扩展可访问的傅里叶带宽克服了这一经典极限。在实验上，我们使用压缩真空探针，在二元假设检验和特征函数重建中均展示了样本复杂度的指数级降低。我们的结果表明，单个玻色子模式可以在没有纠缠或系统尺寸增加的情况下展现出指数级的量子学习优势，从而将可访问的傅里叶带宽确定为量子增强学习中一种根本不同的资源。
英文摘要
Quantum resources can dramatically reduce the data required to learn physical systems, with exponential improvements in sample complexity demonstrated in several quantum learning tasks. However, these advantages have typically relied on quantum resources that scale with problem complexity, most notably increasing system dimension or entanglement. This raises a fundamental question: can exponential quantum learning advantages arise within a fixed, unentangled quantum system? In this paper, we address this question by considering the learning of an unknown random-displacement distribution whose complexity is determined not by the dimensionality of the physical system, but by the Fourier resolution of its features. We show that the quantum-limited noise of vacuum probes progressively obscures high-frequency features, leading to an exponential growth in sample complexity. We establish an information-theoretic lower bound for arbitrary classical-state probes and show that squeezing overcomes this classical limit by extending the accessible Fourier bandwidth. Experimentally, we demonstrate an exponential reduction in sample complexity using squeezed vacuum probes for both binary hypothesis testing and characteristic-function reconstruction. Our results show that a single bosonic mode can exhibit exponential quantum learning advantages without entanglement or an increase in system size, identifying accessible Fourier bandwidth as a fundamentally distinct resource for quantum-enhanced learning.
Comments9 pages, comments and suggestions very welcome
