arXiv：cs.LG· Arka Prabha Das, Abram Magner·· 4 小时前AI 评分26
量子测量 PAC 学习：纠缠学习规则相比单拷贝规则的优势
Advantage of Entangled Learning Rules in Quantum Measurement Class Learning
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研究探讨在量子测量 PAC 学习中使用无法由 LOCC 实现的纠缠测量作为学习规则的优势。作者构造出单拷贝学习规则渐近次优的学习场景，并证明（在自然的联合可测量性覆盖假设下）基于纠缠测量的学习规则相比单拷贝规则最多只有多项式级的样本复杂度优势。
正文
Abstract:Learning with data in the form of quantum states is of current interest and has led to a variety of problems that boil down to interaction with the available data via quantum measurement and classical post-processing of observed classical outcomes. In quantum measurement PAC learning, one is given a sequence of unknown, prepared quantum states and classical labels, along with a hypothesis class of candidate measurements. The task is to select a measurement from the hypothesis class that minimizes a fixed notion of error in prediction of the classical labels via measurement of a new state by the selected hypothesis. In this work, we consider the advantage of interacting with the given data in the measurement learning framework using learning rules given by measurements that cannot be implemented using local operations and classical communication (LOCC), as opposed to single-copy learning rules. We provide a construction showing that there exist learning scenarios wherein single-copy learning rules are asymptotically suboptimal compared to optimal ones. We then show that learning rules based on entangled measurements enjoy at most a polynomial sample complexity advantage over single-copy learning rules in the PAC learning setting (under a natural joint measurability covering assumption).
| Comments: | 9 pages |
| Subjects: | Quantum Physics (quant-ph); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.07328 [quant-ph] |
| (or arXiv:2610.07328v1 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2610.07328 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Abram Magner [view email]
[v1]
Mon, 5 Oct 2026 20:00:46 UTC (84 KB)
来源：arXiv：cs.LG · arxiv.org