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Irreducibly $S U (2)$ $S U (2)$ -covariant quantum channels of low rank

Euijung Chang

Department of Mathematics Education, Seoul National University, Gwanak-Ro 1, Gwanak-Gu, Seoul 08826, Republic of Korea

E-mail Address: uijeong97@snu.ac.kr

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Jaeyoung Kim

https://orcid.org/0000-0002-5706-9864

Department of Mathematics Education, Seoul National University, Gwanak-Ro 1, Gwanak-Gu, Seoul 08826, Republic of Korea

E-mail Address: young15360@snu.ac.kr

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Hyesun Kwak

Department of Mathematics Education, Seoul National University, Gwanak-Ro 1, Gwanak-Gu, Seoul 08826, Republic of Korea

E-mail Address: hskwak@snu.ac.kr

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Hun Hee Lee

Department of Mathematical Sciences and The Research Institute of Mathematics, Seoul National University, Gwanak-Ro 1, Gwanak-gu, Seoul 08826, Republic of Korea

E-mail Address: hunheelee@snu.ac.kr

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, and

Sang-Gyun Youn

https://orcid.org/0000-0003-4411-2381

Department of Mathematics Education, Seoul National University, Gwanak-Ro 1, Gwanak-Gu, Seoul 08826, Republic of Korea

E-mail Address: s.youn@snu.ac.kr

Corresponding author.

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https://doi.org/10.1142/S0129055X22500210Cited by:3 (Source: Crossref)

Abstract

We investigate information theoretic properties of low rank (less than or equal to 3) quantum channels with $S U (2)$ $S U (2)$ -symmetry, where we have a complete description. We prove that PPT property coincides with entanglement-breaking property and that degradability seldomly holds in this class. In connection with these results, we will demonstrate how we can compute Holevo and coherent information of those channels. In particular, we exhibit a strong form of additivity violation of coherent information, which resembles the superactivation of coherent information of depolarizing channels.

Keywords:

AMSC: 81P45, 20C35, 46N50

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