中国物理B ›› 2024, Vol. 33 ›› Issue (10): 100306-100306.doi: 10.1088/1674-1056/ad7c2f

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Freezing imaginarity of quantum states based on 1-norm

Shuo Han(韩烁), Bingke Zheng(郑冰轲), and Zhihua Guo(郭志华)†   

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China
  • 收稿日期:2024-08-04 修回日期:2024-09-11 接受日期:2024-09-18 发布日期:2024-09-30
  • 通讯作者: Zhihua Guo E-mail:guozhihua@snnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 12271325) and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2020JM-294).

Freezing imaginarity of quantum states based on 1-norm

Shuo Han(韩烁), Bingke Zheng(郑冰轲), and Zhihua Guo(郭志华)†   

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China
  • Received:2024-08-04 Revised:2024-09-11 Accepted:2024-09-18 Published:2024-09-30
  • Contact: Zhihua Guo E-mail:guozhihua@snnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 12271325) and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2020JM-294).

摘要: We discuss freezing of quantum imaginarity based on $\ell_1$-norm. Several properties about a quantity of imaginarity based on $\ell_1$-norm are revealed. For a qubit (2-dimensional) system, we characterize the structure of real quantum operations that allow for freezing the quantity of imaginarity of any state. Furthermore, we characterize the structure of local real operations which can freeze the quantity of imaginarity of a class of $N$-qubit quantum states.

关键词: imaginarity freezing, $\ell_1$-norm, real operation

Abstract: We discuss freezing of quantum imaginarity based on $\ell_1$-norm. Several properties about a quantity of imaginarity based on $\ell_1$-norm are revealed. For a qubit (2-dimensional) system, we characterize the structure of real quantum operations that allow for freezing the quantity of imaginarity of any state. Furthermore, we characterize the structure of local real operations which can freeze the quantity of imaginarity of a class of $N$-qubit quantum states.

Key words: imaginarity freezing, $\ell_1$-norm, real operation

中图分类号:  (Entanglement and quantum nonlocality)

  • 03.65.Ud
03.67.Mn (Entanglement measures, witnesses, and other characterizations)