有界广义相对熵：非渐近量子速度极限
Bounding generalized relative entropies: Nonasymptotic quantum speed limits
摘要：
为了更好地理解量子力学，信息论已经成为一个越来越重要的研究领域。值得注意的是，它涵盖了基础和应用的角度，也提供了一个共同的技术语言来研究各种研究领域。值得注意的是，相对熵是信息论中的一个关键量，它量化了区分两个概率分布，甚至两个量子态的难度。这样的量是计量学、量子热力学、量子通信和量子信息等领域的核心。考虑到应用的广泛性，人们希望了解这个量在量子过程中如何变化。通过考虑一般的酉信道，我们建立了信道输出和输入之间的广义相对熵（Rényi和Tsallis）的界。作为我们的界限的应用，我们导出了一个家庭的量子速度限制的基础上相对熵。简要讨论了这个族与热力学、量子相干性、不对称性和单次信息理论之间的可能联系。
英文摘要：
Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language to study a variety of research areas. Remarkably, one of the key information-theoretic quantities is given by the relative entropy, which quantifies how difficult is to tell apart two probability distributions, or even two quantum states. Such a quantity rests at the core of fields like metrology, quantum thermodynamics, quantum communication and quantum information. Given this broadness of applications, it is desirable to understand how this quantity changes under a quantum process. By considering a general unitary channel, we establish a bound on the generalized relative entropies (Rényi and Tsallis) between the output and the input of the channel. As an application of our bounds, we derive a family of quantum speed limits based on relative entropies. Possible connections between this family with thermodynamics, quantum coherence, asymmetry and single-shot information theory are briefly discussed.
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