Triangle-like inequalities related to coherence and entanglement negativity

Abstract

Quantum coherence and entanglement are two key features in quantum mechanics and play important roles in quantum information processing and quantum computation. We provide a general triangle-like inequality satisfied by the \(l_1\)-norm measure of coherence for convex combination of arbitrary n pure states of a quantum state \(\rho \). Furthermore, we present triangle-like inequality for the convex-roof extended negativity for any states of rank 2, which gives a positive answer to a conjecture raised in Dai et al. (Phys. Rev. A 96:062308, 2017). Detailed examples are given to illustrate the relations characterized by the triangle-like inequalities.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments which helped to improve the results of the manuscript. This work is supported by the NSF of China under Grant No. 11675113 and NSF of Beijing under No. KZ201810028042.

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Correspondence to Zhi-Xiang Jin.

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Jin, Z., Li-Jost, X. & Fei, S. Triangle-like inequalities related to coherence and entanglement negativity. Quantum Inf Process 18, 5 (2019). https://doi.org/10.1007/s11128-018-2121-5

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Keywords

  • Triangle-like inequality
  • Quantum coherence
  • Convex-roof extended negativity