Genuine quantum coherence

Abstract

Any quantum resource theory is based on free states and free operations,\ni.e., states and operations which can be created and performed at no cost. In\nthe resource theory of coherence free states are diagonal in some fixed basis,\nand free operations are those which cannot create coherence for some particular\nexperimental realization. Recently, some problems of this approach have been\ndiscussed, and new sets of operations have been proposed to resolve these\nproblems. We propose here the framework of genuine quantum coherence. This\napproach is based on a simple principle: we demand that a genuinely incoherent\noperation preserves all incoherent states. This framework captures coherence\nunder additional constrains such as energy preservation and all genuinely\nincoherent operations are incoherent regardless of their particular\nexperimental realization. We also introduce the full class of operations with\nthis property, which we call fully incoherent. We analyze in detail the\nmathematical structure of these classes and also study possible state\ntransformations. We show that deterministic manipulation is severely limited,\neven in the asymptotic settings. In particular, this framework does not have a\nunique golden unit, i.e., there is no single state from which all other states\ncan be created deterministically with the free operations. This suggests that\nany reasonably powerful resource theory of coherence must contain free\noperations which can potentially create coherence in some experimental\nrealization.\n