School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia.
Institute for Quantum Information and Matter, Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125, USA.
Nat Commun. 2016 May 9;7:11419. doi: 10.1038/ncomms11419.
The quantum capacity of a memoryless channel determines the maximal rate at which we can communicate reliably over asymptotically many uses of the channel. Here we illustrate that this asymptotic characterization is insufficient in practical scenarios where decoherence severely limits our ability to manipulate large quantum systems in the encoder and decoder. In practical settings, we should instead focus on the optimal trade-off between three parameters: the rate of the code, the size of the quantum devices at the encoder and decoder, and the fidelity of the transmission. We find approximate and exact characterizations of this trade-off for various channels of interest, including dephasing, depolarizing and erasure channels. In each case, the trade-off is parameterized by the capacity and a second channel parameter, the quantum channel dispersion. In the process, we develop several bounds that are valid for general quantum channels and can be computed for small instances.
无记忆信道的量子容量决定了我们可以在渐近多次使用该信道进行可靠通信的最大速率。在这里，我们说明在实际情况下，这种渐近特性是不充分的，因为退相干严重限制了我们在编码器和解码器中操纵大型量子系统的能力。在实际环境中，我们应该关注三个参数之间的最优权衡：码率、编码器和解码器中量子器件的大小以及传输的保真度。我们找到了针对各种感兴趣信道（包括相位退相干、极化耗散和擦除信道）的这种权衡的近似和精确描述。在每种情况下，权衡都由容量和第二个信道参数——量子信道弥散度来参数化。在此过程中，我们开发了几个对于一般量子信道有效的界，并且可以对小实例进行计算。
