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Brief Report

Common Coherence Witnesses and Common Coherent States

by 1,*, 2,3, 2,3,* and 4,5,*
1
School of Computer Science and Technology, Guangdong University of Technology, Guangzhou 510006, China
2
School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China
3
Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
4
School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
5
Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany
*
Authors to whom correspondence should be addressed.
Academic Editor: Leong Chuan Kwek
Entropy 2021, 23(9), 1136; https://doi.org/10.3390/e23091136
Received: 30 July 2021 / Revised: 28 August 2021 / Accepted: 30 August 2021 / Published: 31 August 2021
We show the properties and characterization of coherence witnesses. We show methods for constructing coherence witnesses for an arbitrary coherent state. We investigate the problem of finding common coherence witnesses for certain class of states. We show that finitely many different witnesses W1,W2,,Wn can detect some common coherent states if and only if i=1ntiWi is still a witnesses for any nonnegative numbers ti(i=1,2,,n). We show coherent states play the role of high-level witnesses. Thus, the common state problem is changed into the question of when different high-level witnesses (coherent states) can detect the same coherence witnesses. Moreover, we show a coherent state and its robust state have no common coherence witness and give a general way to construct optimal coherence witnesses for any comparable states. View Full-Text
Keywords: common coherence witnesses; high-level witnesses; common coherent states common coherence witnesses; high-level witnesses; common coherent states
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MDPI and ACS Style

Wang, B.-H.; Ding, Z.-H.; Ma, Z.; Fei, S.-M. Common Coherence Witnesses and Common Coherent States. Entropy 2021, 23, 1136. https://doi.org/10.3390/e23091136

AMA Style

Wang B-H, Ding Z-H, Ma Z, Fei S-M. Common Coherence Witnesses and Common Coherent States. Entropy. 2021; 23(9):1136. https://doi.org/10.3390/e23091136

Chicago/Turabian Style

Wang, Bang-Hai, Zi-Heng Ding, Zhihao Ma, and Shao-Ming Fei. 2021. "Common Coherence Witnesses and Common Coherent States" Entropy 23, no. 9: 1136. https://doi.org/10.3390/e23091136

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