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Finite Blocklength Converse Bounds for Quantum Channels

机译:量子通道的有限块长逆边界

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摘要

We derive upper bounds on the rate of transmission of classical information over quantum channels by block codes with a given blocklength and error probability, for both entanglement-assisted and unassisted codes, in terms of a unifying framework of quantum hypothesis testing with restricted measurements. Our bounds do not depend on any special property of the channel (such as memorylessness) and generalize both a classical converse of Polyanskiy, Poor, and Verdú as well as a quantum converse of Renner and Wang, and have a number of desirable properties. In particular, our bound on entanglement-assisted codes is a semidefinite program and for memoryless channels, its large blocklength limit is the well-known formula for entanglement-assisted capacity due to Bennett, Shor, Smolin, and Thapliyal.
机译:对于纠缠辅助代码和非辅助代码,我们通过具有受限测量的量子假设测试的统一框架,得出了具有给定块长和错误概率的块码在量子信道上经典信息传输速率的上限。我们的界限不依赖于通道的任何特殊属性(例如无记忆性),并且泛化了Polyanskiy,Poor和Verdú的经典逆过程以及Renner和Wang的量子逆过程,并具有许多理想的属性。特别地,我们在纠缠辅助代码上的界限是一个半定程序,对于无记忆通道,由于Bennett,Shor,Smolin和Thapliyal,其较大的块长限制是众所周知的纠缠辅助能力公式。

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