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Ordering states of \(l_1\) norm and \(\alpha \)-affinity of coherence

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Abstract

Quantum coherence is the basic characteristic of quantum mechanics. It is an important task to order states with various coherence measures. We investigate the order relations between the \(l_{1}\) norm of coherence and the \(\alpha \)-affinity of coherence for quantum states. We find that the \(l_{1}\) norm of coherence and any \(\alpha \)-affinity of coherence provide the same ordering for qubit pure states and maximally coherent mixed qubit states. We also show that there exist some qubit states which give rise to different ordering under the \(l_{1}\) norm of coherence and any \(\alpha \)-affinity of coherence. In addition, the \(l_{1}\) norm of coherence and \(\alpha \)-affinity of coherence do not generate the same ordering for some high-dimensional pure states, but they do for some special X states of two-qubit systems.

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Correspondence to Yuan-Hong Tao.

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S.-M. Fei: This work is supported by NSFC under Nos. 11761073, 11675113 and 12075159, Beijing Municipal Commission of Education (KZ201810028042), Beijing Natural Science Foundation (Grant No. Z190005); Academy for Multidisciplinary Studies, Capital Normal University; Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China (No. SIQSE202001).

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Zhang, J., Sheng, YH., Tao, YH. et al. Ordering states of \(l_1\) norm and \(\alpha \)-affinity of coherence. Quantum Inf Process 20, 98 (2021). https://doi.org/10.1007/s11128-021-03026-y

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