The smooth entropy formalism for von Neumann algebras
The smooth entropy formalism for von Neumann algebras
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DOI：
10.1063/1.4936405
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发表时间：
2016-01-01
影响因子：
1.3
通讯作者：
Scholz, Volkher B.
中科院分区：
文献类型：
--
作者：
Berta, Mario;Furrer, Fabian;Scholz, Volkher B.
我们讨论了无限维量子系统的信息论概念。特别地，我们将Renner和合作者为有限维系统引入的光滑熵形式推广到von Neumann代数。对于光滑的条件最小和最大熵，我们得到了与有限维情形类似的刻画性质和信息论运算解释。我们推广了Tomamichel和Renner的量子边信息与熵不确定关系，并讨论了它在量子密码学中的应用。特别是，我们证明了用von Neumann代数建模的量子边信息进行隐私放大和经典数据压缩的可能性。(C)2015 AIP出版有限责任公司。
We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra. (C) 2015 AIP Publishing LLC.