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

Taro Shibayama; Yingkai Ouyang

doi:10.1109/itw48936.2021.9611450

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arXiv · 2105.07214

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

Taro Shibayama·Yingkai Ouyang

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Abstract

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.

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Taro Shibayama, Yingkai Ouyang. 2021-05-15. The equivalence between correctability of deletions and insertions of separable states in quantum codes. https://doi.org/10.1109/itw48936.2021.9611450

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