arXiv quant-ph/04041062004-04quant-ph

稳定子码的局部不变量

Local invariants of stabilizer codes

Maarten Van den Nest, Jeroen Dehaene, Bart De Moor

备注：: 10 pages, 1 figure. Minor changes. Accepted in Phys. Rev. A
发表信息：: Phys. Rev A 70, 032323 (2004)
DOI：: 10.1103/PhysRevA.70.032323

摘要：

在[Phys.Rev.A58，1833（1998）]中，提出了一族多项式不变量，它们在局域幺正群的作用下分离多量子比特密度算符$ρ$的轨道。我们认为这个家庭的不变量的类的那些$ρ$这是投影算子描述稳定器代码，并给出一个完整的翻译这些不变量到二进制框架中，稳定器代码通常描述。量子码的局部不变量的研究在量子编码理论中具有自然的重要性，因为局部等价码具有相同的纠错能力，并且局部不变量是探索其结构的强大工具。此外，目前的结果是相关的多体纠缠的背景下，并被称为单向量子计算机的量子计算的测量为基础的模型的发展。

英文摘要：

In [Phys. Rev. A 58, 1833 (1998)] a family of polynomial invariants which separate the orbits of multi-qubit density operators $ρ$ under the action of the local unitary group was presented. We consider this family of invariants for the class of those $ρ$ which are the projection operators describing stabilizer codes and give a complete translation of these invariants into the binary framework in which stabilizer codes are usually described. Such an investigation of local invariants of quantum codes is of natural importance in quantum coding theory, since locally equivalent codes have the same error-correcting capabilities and local invariants are powerful tools to explore their structure. Moreover, the present result is relevant in the context of multipartite entanglement and the development of the measurement-based model of quantum computation known as the one-way quantum computer.

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