Current browse context:
quant-ph
Change to browse by:
References & Citations
Quantum Physics
Title: Operational Interpretation of the Sandwiched Rényi Divergence of Order 1/2 to 1 as Strong Converse Exponents
(Submitted on 1 Sep 2022 (v1), last revised 28 May 2024 (this version, v5))
Abstract: We provide the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of quantum tasks. Specifically, we consider (a) smoothing of the max-relative entropy, (b) quantum privacy amplification, and (c) quantum information decoupling. We solve the problem of determining the exact strong converse exponents for these three tasks, with the performance being measured by the fidelity or purified distance. The results are given in terms of the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, and its induced quantum R\'enyi conditional entropy and quantum R\'enyi mutual information. This is the first time to find the precise operational meaning for the sandwiched R\'enyi divergence with R\'enyi parameter in the interval $\alpha\in(\frac{1}{2},1)$.
Submission history
From: Yongsheng Yao [view email][v1] Thu, 1 Sep 2022 15:57:10 GMT (32kb)
[v2] Thu, 8 Dec 2022 12:21:22 GMT (32kb)
[v3] Tue, 16 Jan 2024 08:09:57 GMT (39kb)
[v4] Tue, 21 May 2024 15:57:36 GMT (39kb)
[v5] Tue, 28 May 2024 06:57:41 GMT (39kb)
Link back to: arXiv, form interface, contact.