Logarithmic coherence: Operational interpretation of l(1)-norm coherence

TitleLogarithmic coherence: Operational interpretation of l(1)-norm coherence
Publication TypeJournal Article
Year of Publication2017
AuthorsRana, S, Parashar, P, Winter, A, Lewenstein, M
JournalPHYSICAL REVIEW A
Volume96
Issue5
ISSN2469-9926
Abstract

We show that the distillable coherence-which is equal to the relative entropy of coherence-is, up to a constant factor, always bounded by the l(1)-norm measure of coherence (defined as the sum of absolute values of off diagonals). Thus the latter plays a similar role as logarithmic negativity plays in entanglement theory and this is the best operational interpretation from a resource-theoretic viewpoint. Consequently the two measures are intimately connected to another operational measure, the robustness of coherence. We find also relationships between these measures, which are tight for general states, and the tightest possible for pure and qubit states. For a given robustness, we construct a state having minimum distillable coherence.

DOI10.1103/PhysRevA.96.052336
Campus d'excel·lència internacional U A B