盲量子数据压缩的指数强逆定理
Exponential strong converse for blind quantum data compression
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中文总结 AI 辅助
本文证明了盲量子数据压缩（含或不含纠缠辅助）在最优速率下的指数强逆定理，引入基于量子态结构的新重叠量，为混合态信息处理任务的逆分析提供工具。
中文摘要 AI 辅助
我们针对有限维混合态源的盲量子数据压缩建立了指数强逆定理，分别考虑了有纠缠辅助和无纠缠辅助两种情况。盲压缩是量子信息处理中的一项基本任务，其中发送方旨在无需直接访问经典标签的情况下传输量子态。强逆是数据压缩的一个显著特性：一旦压缩率低于某个阈值，压缩的精度会突然降至零。对于纯态源，数据压缩的强逆定理已经建立；然而，对于混合态源，最优压缩率由量子态的结构分解决定，并且可能在小的扰动下发生显著变化。这种敏感性使得定量分析压缩率与误差之间的权衡变得困难。尽管近期取得了进展，但在最优速率下强逆是否成立的问题在一般情况下仍未解决。在本工作中，我们肯定地回答了这个问题。对于无辅助压缩，我们证明在低于最优值的每个速率下，对于一般混合态源，精度随块长度指数衰减，且对协议没有限制。我们还证明了在最优速率下，具有无限纠缠辅助的盲压缩的指数强逆。将这两个强逆界结合起来，可以得到在完整可达速率区域之外的每个压缩-纠缠速率对上的指数衰减。我们的证明引入了一个基于量子态结构的新重叠量；该量将源信息的保持与传输系统的维度联系起来。我们期望这种方法能为涉及混合态的其他量子信息处理任务的逆分析提供有用的工具。
英文摘要
We establish exponential strong converse theorems for blind quantum data compression of finite-dimensional mixed-state sources, with and without entanglement assistance. Blind compression is a fundamental quantum information processing task in which the sender aims to transmit quantum states without direct access to the classical label. Strong converse is a notable aspect of data compression: the accuracy of the compression abruptly drops down to zero once the compression rate goes below a threshold. Strong converses for data compression have been established for pure-state sources; however, for mixed-state sources, the optimal compression rate is determined by a structural decomposition of quantum states and can change substantially under small perturbations. This sensitivity makes it difficult to quantitatively analyze the trade-off between compression rate and error. Despite recent progress, whether a strong converse holds at the optimal rate has remained unresolved in general. In this work, we resolve this question affirmatively. For unassisted compression, we show that at every rate below the optimum, the accuracy decays exponentially with the block length for general mixed-state sources without restrictions on protocols. We also prove exponential strong converse for blind compression with unlimited entanglement assistance at its optimal rate. Combining the two strong converse bounds yields exponential decay at every compression-entanglement rate pair outside the complete achievable rate region. Our proof introduces a new overlap quantity based on the structure of quantum states; this quantity connects preservation of the source information to the dimension of the transmitted system. We expect that this approach provides useful tools for converse analyses of other quantum information-processing tasks involving mixed states.
发表机构
- University of Waterloo（滑铁卢大学）
- Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
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