Operational Interpretations of the l1 Norm Coherence in Pure Quantum Systems

Abstract

The operational property of quantum coherence plays an important role in the development of the coherent resource theory. As one of the qualified measures of coherence, the l1 norm of coherence is easily computable, but it is difficult to find an intuitionistic interpretation. In this paper, we provide operational interpretations of the l1 norm of coherence as coherence distillation and discriminating subchannels separately. From the view of coherence distillation, the l1 norm of coherence is directly related to the maximum distance between the given state and the maximally coherent state under some incoherent operation, so it can be reviewed as the distillation of coherence from the given state. In the aspect of the subchannel discrimination, the l1 norm of coherence can characterize the advantage of coherent states in subchannel discrimination, because any coherent state provide a higher probability of successful discriminating subchannels than that of all incoherent states.