01224nas a2200169 4500008004100000245005300041210005300094260001500147300001100162490000700173520074800180100001800928700002400946700001800970700001900988856004701007 2016 eng d00aQuantifying the coherence of pure quantum states0 aQuantifying the coherence of pure quantum states c2016/10/07 a0423130 v943 a
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.
1 aChen, Jianxin1 aJohnston, Nathaniel1 aLi, Chi-Kwong1 aPlosker, Sarah uhttps://doi.org/10.1103/PhysRevA.94.042313