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Notes on quantum coherence with \(l_1\)-norm and convex-roof \(l_1\)-norm

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Abstract

In this work, we evaluate quantum coherence using the \(l_{1}\)-norm and convex-roof \(l_{1}\)-norm and obtain several new results. First, we provide some new general triangle-like inequalities of quantum coherence, with results better than existing ones. Second, for some special three-dimensional quantum states, a method for calculating the convex-roof \(l_{1}\)-norm is presented. Lastly, we offer distinct upper bounds in the \(l_{1}\)-norm measure of coherence based on the quantum state itself.

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Acknowledgements

This work is supported by Hainan Provincial Natural Science Foundation of China under Grant Nos. 121RC539 and 121MS030; and by the National Natural Science Foundation of China under Grant No. 11861031. This project is also supported by the Innovation Platform for Academicians of Hainan Province.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, China

    Jiayao Zhu, Jian Ma & Tinggui Zhang

  2. Key Laboratory of Data Science and Smart Education, Ministry of Education, Hainan Normal University, Haikou, 571158, China

    Jian Ma & Tinggui Zhang

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  1. Jiayao Zhu
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  2. Jian Ma
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  3. Tinggui Zhang
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Correspondence to Tinggui Zhang.

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Zhu, J., Ma, J. & Zhang, T. Notes on quantum coherence with \(l_1\)-norm and convex-roof \(l_1\)-norm. Quantum Inf Process 20, 400 (2021). https://doi.org/10.1007/s11128-021-03325-4

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