Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. We introduce two new families of quantum convolutional codes. Our construction is based on an algebraic method which allows to construct classical convolutional codes from block codes, in particular BCH codes. These codes have the property that they contain their Euclidean, respectively Hermitian, dual codes. Hence, they can be used to define quantum convolutional codes by the stabilizer code construction. We compute BCH-like bounds on the free distances which can be controlled as in the case of block codes, and establish that the codes have non-catastrophic encoders.
Quantum $(r,δ)$-Locally Recoverable BCH and Homothetic-BCH Codes
Instituto Universitario de Matemáticas y Aplicaciones de Castellón and Departamento de Matemáticas, Universitat Jaume I（卡斯特利翁数学与应用大学研究所及卡斯特利翁大学数学系）；Department of Information and Communications Engineering, Institute of Science Tokyo（东京科学大学信息与通信工程系）
The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable than qudit-flip errors. Moreover, they use pre-shared entanglement between encoder and decoder to simplify the theory of quantum error correction and increase the communication capacity. Thus, asymmetric EAQECCs can be constructed from any pair of classical linear codes over an arbitrary field. Their parameters are described and a Gilbert-Varshamov bound is…
在本文中，我们展示了如何构造新的卷积码从旧的应用众所周知的技术：打孔，扩展，扩大，直接和，（u| u + v）构造和乘积码构造。通过应用这些方法，可以构造几个新的卷积码族。作为码扩展的一个例子，构造了从经典的Bose-Chaudhuri-Hocquenghem（BCH）、特征码和Melas码导出的卷积码族。
A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name of quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the ensemble of channels. Classical and quantum codes can be envisioned for this goal. The aim of this paper is to present a simple but fruitful protocol for this task using classical error-correcting codes. Three families of codes are considered: Reed-Solomon codes, BCH codes, and Reed-Muller codes. In conjunction to the use of codes, we also analyze the role o…
In this paper, we present two new ways of quantum synchronization coding based on the $(\bm{u}+\bm{v}|\bm{u}-\bm{v})$ construction and the product construction respectively, and greatly enrich the varieties of available quantum synchronizable codes. The circumstances where the maximum synchronization error tolerance can be reached are explained for both constructions. Furthermore, repeated-root cyclic codes derived from the $(\bm{u}+\bm{v}|\bm{u}-\bm{v})$ construction are shown to be able to provide better Pauli error-correcting capability than BCH codes.
Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional stabilizer formalism. In this paper, it is shown a general method to construct QUENTA codes from cyclic codes. Afterwards, the method is applied to Reed-Solomon codes, BCH codes, and general cyclic codes. We use the Euclidean and Hermitian construction of QUENTA codes. Two families of QUENTA codes are maximal distance separable (MDS), and one is almost MDS or alm…
在量子信息处理中，相移误差比量子位翻转误差发生的概率更大，因而前者对量子信息的干扰更大。这使得我们构造了非对称量子差错控制码$\Pr Z \geq \Pr X$来保护非对称信道上的量子信息。本文提出了两种利用生成多项式和定义经典循环码集合导出非对称量子循环码的一般方法。因此，该方法使我们能够构建几个家庭的非对称量子BCH，RS和RM码。最后，利用这些方法构造了非对称子系统码族。
