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Assessing the role of interference in natural and artificial quantumdyanamical processes is a crucial task in quantum information theory. To thisaim, an appopriate formalism is provided by the decoherent histories framework.While this approach has been deeply explored from different theoreticalperspectives, it still lacks of a comprehensive set of tools able to conciselyquantify the amount of coherence developed by a given dynamics. In this paperwe introduce and test different measures of the (average) coherence present indissipative (Markovian) quantum evolutions, at various time scales and fordifferent levels of environmentally induced decoherence. In order to show theeffectiveness of the introduced tools, we apply them to a paradigmatic quantumprocess where the role of coherence is being hotly debated: exciton transportin photosynthetic complexes. To spot out the essential features that maydetermine the performance of the transport we focus on a relevant trimericsubunit of the FMO complex and we use a simplified (Haken-Strobl) model for thesystem-bath interaction. Our analysis illustrates how the high efficiency ofenvironmentally assisted transport can be traced back to a quantum recoilavoiding effect on the exciton dynamics, that preserves and sustains thebenefits of the initial fast quantum delocalization of the exciton over thenetwork. Indeed, for intermediate levels of decoherence, the bath is seen toselectively kill the negative interference between different exciton pathways,while retaining the initial positive one. The concepts and tools here developedshow how the decoherent histories approach can be used to quantify the relationbetween coherence and efficiency in quantum dynamical processes.

Global coherence of quantum evolutions based on decoherent histories: theory and application to photosynthetic quantum energy transport