arXiv 1101.24092011-01-12quant-ph

量化量子码的性能

Quantifying the Performance of Quantum Codes

C. Cafaro, S. L'Innocente, C. Lupo, S. Mancini

备注：: 21 pages, 10 figures
发表信息：: Open Sys. & Information Dyn. 18, 1 (2011)
DOI：: 10.1142/S1230161211000029

摘要：

利用纠缠保真度和码熵研究了噪声模型下存在非对称性和相关性时纠错码的性质。首先，我们考虑了一个退相马尔可夫记忆信道和表征的性能的重复码和避免错误的码的纠缠保真度。我们还考虑了这样的代码的级联，并表明，它是特别有利的制度的偏相关。最后，我们的代码和他们的级联的代码熵的装置的有效性的特征，并发现，特别是，恢复这样的代码所需的努力减少时，错误概率降低和内存参数增加。其次，我们考虑了对称和非对称去极化噪声量子存储信道，并通过五量子比特稳定码进行量子纠错。我们通过纠缠保真度和码熵作为非对称错误概率和记忆度的函数来表征这种码。具体来说，我们发现，虽然去极化误差的不对称性不影响五量子比特码的纠缠保真度，但当码熵用作性能量化器时，它成为一个相关的特征。

英文摘要：

We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and characterize the performance of both a repetition code and an error avoiding code in terms of the entanglement fidelity. We also consider the concatenation of such codes and show that it is especially advantageous in the regime of partial correlations. Finally, we characterize the effectiveness of the codes and their concatenation by means of the code entropy and find, in particular, that the effort required for recovering such codes decreases when the error probability decreases and the memory parameter increases. Second, we consider both symmetric and asymmetric depolarizing noisy quantum memory channels and perform quantum error correction via the five qubit stabilizer code. We characterize this code by means of the entanglement fidelity and the code entropy as function of the asymmetric error probabilities and the degree of memory. Specifically, we uncover that while the asymmetry in the depolarizing errors does not affect the entanglement fidelity of the five qubit code, it becomes a relevant feature when the code entropy is used as a performance quantifier.

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