提出可计算的量子隐私度量，用于实际测量限制下的隐私保护分析。
Measured Hockey-Stick Divergence and its Applications to Quantum Pufferfish Privacy
- 定义并分析受限测量下的霍克斯特克散度，结合半定规划实现高效计算。
- 证明其在威纳和各向同性态下可解析求解，且具数据处理与凸性性质。
- 首次建立其与量子河豚隐私框架的关联，适用于真实场景的隐私审计。
霍克斯特克散度是刻画经典与量子数据隐私框架的核心量。传统量子隐私模型允许对手执行任意测量，但实际中测量能力受限。本文系统研究了多种实用测量类下的受限制霍克斯特克散度，证明其具备数据处理不等式与凸性。对于部分测量类，该散度可通过半定规划高效计算；对威纳（Werner）和各向同性（isotropic）态，可解析求解。特别地，本文揭示其能表征量子河豚隐私（quantum pufferfish privacy）框架中的最优隐私参数。基于此联系及所发展工具，实现了对多个实际场景的隐私量化与审计方法。最后引入通道的受限制霍克斯特克散度，并探讨其在通道隐私保障中的应用。
原文摘要 · Abstract (English)
The hockey-stick divergence is a fundamental quantity characterizing several statistical privacy frameworks that ensure privacy for classical and quantum data. In such quantum privacy frameworks, the adversary is allowed to perform all possible measurements. However, in practice, there are typically limitations to the set of measurements that can be performed. To this end, here, we comprehensively analyze the measured hockey-stick divergence under several classes of practically relevant measurement classes. We prove several of its properties, including data processing and convexity. We show that it is efficiently computable by semi-definite programming for some classes of measurements and can be analytically evaluated for Werner and isotropic states. Notably, we show that the measured hockey-stick divergence characterizes optimal privacy parameters in the quantum pufferfish privacy framework. With this connection and the developed technical tools, we enable methods to quantify and audit privacy for several practically relevant settings. Lastly, we introduce the measured hockey-stick divergence of channels and explore its applications in ensuring privacy for channels.
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