Brun Todd, Devetak Igor, Hsieh Min-Hsiu
Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA.
Science. 2006 Oct 20;314(5798):436-9. doi: 10.1126/science.1131563. Epub 2006 Sep 28.
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error-correcting codes, thus allowing us to "quantize" all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement enables quantum communication.
我们展示了编码器和解码器之间共享的纠缠如何能够简化量子纠错理论。我们所描述的纠缠辅助量子码不需要标准量子纠错码所必需的包含对偶的约束条件，从而使我们能够“量化”所有经典线性编码理论。特别地，达到香农容量的高效现代经典码可以被制成达到哈希界（与量子容量密切相关）的纠缠辅助量子码。对于没有大量共享纠缠的系统，这些码也可以用作催化码，其中少量的初始纠缠就能实现量子通信。
