Average skew information-based coherence and its typicality for random quantum states
Zhaoqi Wu, Lin Zhang, Shao-Ming Fei, and Xianqing Li-Jost
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Submission date: 30. Oct. 2019
PACS-Numbers: 03.65.Ud, 03.67.-a, 03.75.Gg
Keywords and phrases: Average coherence, skew information, random quantum states, typicality
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We study the average skew information-based coherence for both random pure and mixed states. The explicit formulae of the average skew information-based coherence are derived and shown to be the functions of the dimension N of the state space. We demonstrate that as N approaches to inﬁnity, the average coherence is 1 for random pure states, and a positive constant less than for random mixed states. We also explore the typicality of average skew information-based coherence of random quantum states. Furthermore, we identify a coherent subspace such that the amount of the skew information based coherence for each pure state in this subspace can be bounded from below almost always by a ﬁxed number that is arbitrarily close to the typical value of coherence.