Operational Resource Theory of Coherence

We establish an operational theory of coherence (or of superposition) in quantum systems, by focusing on the optimal rate of performance of certain tasks. Namely, we introduce the two basic concepts-"coherence distillation" and "coherence cost"-in the processing quantum states under so-called incoherent operations [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. We, then, show that, in the asymptotic limit of many copies of a state, both are given by simple single-letter formulas: the distillable coherence is given by the relative entropy of coherence (in other words, we give the relative entropy of coherence its operational interpretation), and the coherence cost by the coherence of…

• NN
  National Natural Science Foundation of China

  Award: 11375165
• GD
  Generalitat de Catalunya

  Award: 2014-SGR-966
• MD
  Ministerio de Economía y Competitividad

  Awards: FIS2013-40627-P, FIS2008-01236
• ER
  European Research Council