Triangle-like inequalities related to coherence and entanglement negativity

Zhi-Xiang Jin, Xianqing Li-Jost, and Shao-Ming Fei

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Submission date: 09. Jan. 2019
Pages: 13
published in: Quantum information processing, 18 (2019) 1, art-no. 5 
DOI number (of the published article): 10.1007/s11128-018-2121-5
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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 l₁-norm measure of coherence for convex combination of arbitrary n pure states of a quantum state ρ. 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 [Phys. Rev. A 96, 062308 (2017)]. Detailed examples are given to illustrate the relations characterized by the triangle-like inequalities.