论文标题
修改从高度纠缠状态构建量子代码的方法
Modifying method of constructing quantum codes from highly entangled states
论文作者
论文摘要
经典代码，高度纠缠的纯状状态（称为k-均匀或绝对最大纠缠（AME）状态）和量子误差校正代码（QECC）之间存在联系。这导致了一种系统的方法，可以从K-均匀状态或相应的经典代码开始并在每个步骤中搜索一个方来构建稳定器QECC。我们通过描述部分痕迹在经典代码的相应发生器矩阵上引起的更改，为QECC提供QECC的代码字，编码过程和稳定器形式的明确构造。然后，我们修改了产生另一组稳定器QECC的方法，该QECC将逻辑Qudit编码为AME状态跨越的子空间。该构建产生从AME状态开始的量子代码，而无需追踪任何政党。因此，可以构建具有较大代码空间的量子稳定器代码。
There is a connection between classical codes, highly entangled pure states (called k-uniform or absolutely maximally entangled (AME) states), and quantum error correcting codes (QECCs). This leads to a systematic method to construct stabilizer QECCs by starting from a k-uniform state or the corresponding classical code and tracing out one party at each step. We provide explicit constructions for codewords, encoding procedure and stabilizer formalism of the QECCs by describing the changes that partial traces cause on the corresponding generator matrix of the classical codes. We then modify the method to produce another set of stabilizer QECCs that encode a logical qudit into a subspace spanned by AME states. This construction produces quantum codes starting from an AME state without tracing out any party. Therefore, quantum stabilizer codes with larger codespace can be constructed.
