%0 Journal Article %J Physical Review A %D 2016 %T Quantifying the coherence of pure quantum states %A Jianxin Chen %A Nathaniel Johnston %A Chi-Kwong Li %A Sarah Plosker %X

In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an explicit characterization of the closest incoherent state to a given pure state under the trace distance measure of coherence, and we affirm a recent conjecture that the ℓ1 measure of coherence of a pure state is never smaller than its relative entropy of coherence. We then use our result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states, and we derive a new inequality relating the negativity and distillable entanglement of pure states.

%B Physical Review A %V 94 %P 042313 %8 2016/10/07 %G eng %U https://doi.org/10.1103/PhysRevA.94.042313 %N 4 %R 10.1103/PhysRevA.94.042313 %0 Journal Article %J New Journal of Physics %D 2015 %T Discontinuity of Maximum Entropy Inference and Quantum Phase Transitions %A Jianxin Chen %A Zhengfeng Ji %A Chi-Kwong Li %A Yiu-Tung Poon %A Yi Shen %A Nengkun Yu %A Bei Zeng %A Duanlu Zhou %X In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit. %B New Journal of Physics %V 17 %P 083019 %8 2015/08/10 %G eng %U http://arxiv.org/abs/1406.5046v2 %N 8 %! New J. Phys. %R 10.1088/1367-2630/17/8/083019