Maximal $α$-Leakage for Quantum Privacy Mechanisms
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914723278094336 |
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| author | Yang, Bo-Yu Yu, Hsuan Cheng, Hao-Chung |
| author_facet | Yang, Bo-Yu Yu, Hsuan Cheng, Hao-Chung |
| contents | In this work, maximal $α$-leakage is introduced to quantify how much a quantum adversary can learn about any sensitive information of data upon observing its disturbed version via a quantum privacy mechanism. We first show that an adversary's maximal expected $α$-gain using optimal measurement is characterized by measured conditional Rényi entropy. This can be viewed as a parametric generalization of König et al.'s famous guessing probability formula [IEEE Trans. Inf. Theory, 55(9), 2009]. Then, we prove that the $α$-leakage and maximal $α$-leakage for a quantum privacy mechanism are determined by measured Arimoto information and measured Rényi capacity, respectively. Various properties of maximal $α$-leakage, such as data processing inequality and composition property are established as well. Moreover, we show that regularized $α$-leakage and regularized maximal $α$-leakage for identical and independent quantum privacy mechanisms coincide with $α$-tilted sandwiched Rényi information and sandwiched Rényi capacity, respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_14450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal $α$-Leakage for Quantum Privacy Mechanisms Yang, Bo-Yu Yu, Hsuan Cheng, Hao-Chung Quantum Physics Cryptography and Security Information Theory In this work, maximal $α$-leakage is introduced to quantify how much a quantum adversary can learn about any sensitive information of data upon observing its disturbed version via a quantum privacy mechanism. We first show that an adversary's maximal expected $α$-gain using optimal measurement is characterized by measured conditional Rényi entropy. This can be viewed as a parametric generalization of König et al.'s famous guessing probability formula [IEEE Trans. Inf. Theory, 55(9), 2009]. Then, we prove that the $α$-leakage and maximal $α$-leakage for a quantum privacy mechanism are determined by measured Arimoto information and measured Rényi capacity, respectively. Various properties of maximal $α$-leakage, such as data processing inequality and composition property are established as well. Moreover, we show that regularized $α$-leakage and regularized maximal $α$-leakage for identical and independent quantum privacy mechanisms coincide with $α$-tilted sandwiched Rényi information and sandwiched Rényi capacity, respectively. |
| title | Maximal $α$-Leakage for Quantum Privacy Mechanisms |
| topic | Quantum Physics Cryptography and Security Information Theory |
| url | https://arxiv.org/abs/2403.14450 |