安全PAC学习：样本预算定律与量子数据路径可采纳性
Secure PAC Learning: Sample-Budget Laws and Quantum Data-Path Admissibility
AI总结：
基于PAC视角提出安全学习理论，将数据路径行为与有限样本预算关联，并在量子信息背景下建立量子安全PAC学习框架，利用Holevo信息阈值实现无经典对应的安全保证。
摘要：
当数据被窃取或受到扰动时，机器学习的安全性是脆弱的，然而现有的框架很少将安全性的定义和分析与可学习性联系起来。在本研究中，我们基于可能近似正确（PAC）的视角发展了一种安全学习理论，并开发了一个将数据路径行为与有限样本预算联系起来的操作框架。在我们的公式中，准确率-置信度目标通过一个基于运行的序贯测试进行评估，该测试在达到规定次数的连续验证后停止，并且如果数据路径信道是可采纳的，则一个闭式预算界限保证了学习成功；其接受度还必须超过一个基本的随机搜索基线。我们在量子信息的背景下提升并完成了我们的安全学习构造——建立了量子安全PAC学习：对于制备与测量场景，数据路径的可采纳性被设定为由Holevo信息固定的阈值，而不是学习者可调的容忍度。因此，学习者获得认证的信息优势直接转化为学习安全性——这是一种经典情况下没有类似效果的现象。由信道确定的置信度自然产生，并且为了实际部署引入了基矢筛选。这是第一个在PAC学习中同时嵌入安全性概念和操作样本预算定律，并将安全性锚定于量子信息的完整框架。由此产生的设计蓝图指向学习安全性的标准化保证，并为PAC-Bayes扩展以及与高级量子机器学习前端的集成提供了明确的途径。
英文摘要：
Security in machine learning is fragile when data are exfiltrated or perturbed, yet existing frameworks rarely connect the definition and analysis of the security to learnability. In this work, we develop a theory of secure learning grounded in the probably-approximately-correct (PAC) viewpoint and develop an operational framework that links data-path behavior to finite-sample budgets. In our formulation, an accuracy-confidence target is evaluated via a run-based sequential test that halts after a prescribed number of consecutive validations, and a closed-form budget bound guarantees the learning success if the data-path channel is admissible; the acceptance must also exceed a primitive random-search baseline. We elevate and complete our secure-learning construction in the context of quantum information -- establishing quantum-secure PAC learning: for prepare-and-measure scenarios, the data-path admissibility is set to be threshold fixed by Holevo information, not a learner-tunable tolerance. Thus, a certified information advantage for the learner directly becomes the learning security -- an effect with no classical analogue. The channel-determined confidence follows naturally and basis sifting is incorporated for practical deployments. This is the first complete framework that simultaneously embeds a security notion and an operational sample-budget law within the PAC learning and anchors the security in quantum information. The resulting blueprint points toward standardized guarantees for the learning security, with clear avenues for PAC-Bayes extensions and for integration with advanced quantum machine learning front ends.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
