A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
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DOI：
10.1109/tit.2013.2276628
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发表时间：
2012-08
影响因子：
2.5
通讯作者：
M. Tomamichel;Masahito Hayashi
中科院分区：
文献类型：
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作者：
M. Tomamichel;Masahito Hayashi
我们考虑了量子信息理论中的两个基本任务，利用量子边信息进行数据压缩，以及利用量子边信息进行随机性提取。我们的特点，这些任务一般来源，使用所谓的一次性熵。这些特点，在对比早期的结果，使我们能够得到严格的二阶渐近这些任务的独立同分布。极限更一般地说，我们的推导建立了一个信息量的层次结构，可用于研究量子领域的信息理论任务：一次性熵最准确地描述了一个操作量，但它们往往难以计算大型系统。我们表明，他们渐近同意（对数项）与熵有关的量子和经典的信息谱，这是更容易计算的i.i.d.极限我们的技术也自然产生有限块长度的操作量的界限。
We consider two fundamental tasks in quantum information theory, data compression with quantum side information, as well as randomness extraction against quantum side information. We characterize these tasks for general sources using so-called one-shot entropies. These characterizations-in contrast to earlier results-enable us to derive tight second-order asymptotics for these tasks in the i.i.d. limit. More generally, our derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain: The one-shot entropies most accurately describe an operational quantity, yet they tend to be difficult to calculate for large systems. We show that they asymptotically agree (up to logarithmic terms) with entropies related to the quantum and classical information spectrum, which are easier to calculate in the i.i.d. limit. Our technique also naturally yields bounds on operational quantities for finite block lengths.