量子删除和插入错误在排列不变码中的等价性

The equivalence between correctability of deletions and insertions of separable states in quantum codes

In this paper, we prove the equivalence of inserting separable quantum states and deletions. Hence any quantum code that corrects deletions automatically corrects separable insertions. First, we describe the quantum insertion/deletion error using the Kraus operators. Next, we develop an algebra for commuting Kraus operators corresponding to insertions and deletions. Using this algebra, we prove the equivalence between quantum insertion codes and quantum deletion codes using the Knill-Laflamme conditions.

构造单个量子dit（qudit）插入/删除码的充要条件及其译码算法

Necessary and sufficient condition for constructing a single qudit insertion/deletion code and its decoding algorithm

本研究将Knill-Laflamme条件推广应用于粒子数变化的量子错误场景，证明单插入与单删除错误可纠错性等价，得到单qudit插入/删除码的充要构造条件，还构造了新码并给出译码算法。

Quantum Insertion-Deletion Channels

We introduce a model of quantum insertion-deletion (insdel) channels. Insdel channels are meant to represent, for example, synchronization errors arising in data transmission. In the classical setting, they represent a strict generalization of the better-understood corruption error channels, and until recently, had mostly resisted effort toward a similar understanding as their corruption counterparts. They have received considerable attention in recent years. Very recently, Haeupler and Shahrasbi developed a framework, using what they call synchronisation strings, that allows one to turn insde…

Permutation-Invariant Quantum Codes for Deletion Errors

This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion errors. Also, our codes give the first example of quantum codes that can correct both multiple-qubit errors and multiple-deletion errors. We also discuss a generalization of the construction of our codes at the end.

Permutation-invariant quantum coding for quantum deletion channels

Quantum deletions, which are harder to correct than erasure errors, occur in many realistic settings. It is therefore pertinent to develop quantum coding schemes for quantum deletion channels. To date, not much is known about which explicit quantum error correction codes can combat quantum deletions. We note that {\em any} permutation-invariant quantum code that has a distance of $t+1$ can correct $t$ quantum deletions for any positive integer $t$ in both the qubit and the qudit setting. Leveraging on coding properties of permutation-invariant quantum codes under erasure errors, we derive corr…

一种针对量子插入错误的角动量方法

An angular momentum approach to quantum insertion errors

针对量子插入错误校正通用框架研究不足的问题，本文提出基于角动量测量的两阶段伴随式提取与隐形传态协议，可在有隙置换不变码上校正单个量子插入错误。