Quantifying coherence of quantum channels via trace distance

Zhen Wang, Yan-Ling Wang, Zhi‐Xi Wang

Lu Li, Kaifeng Bu, Zi-Wen Liu

We propose a general method to operationally quantify the ``resourcefulness'' of quantum channels via channel discrimination, an important information processing task. A main result is that the maximum success probability of distinguishing a given channel from the set of free channels by free probe states is exactly characterized by the resource generating power, i.e., the maximum amount of resource produced by the action of the channel, given by the trace distance to the set of free states. We apply this framework to the resource theory of quantum coherence, as an informative example. The general results can also be easily applied to other resource theories such as entanglement, magic states, and asymmetry.

Yajing Fan, Lulu Li

Jianxin Chen, Shane Grogan, Nathaniel Johnston +2 more

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. We then use this result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states. We define the trace distance of entanglement and show that it coincides with the trace distance of coherence for pure states. Finally, we give an alternate proof to a recent result that the ${\ensuremath{\ell}}_{1}$ measure of coherence of a pure state is never smaller than its relative entropy of coherence.

Shi-Yun Kong, Ya-Juan Wu, Qiao-Qiao Lv +2 more

Chandan Datta, Sk Sazim, Arun Kumar Pati +1 more