We review various methods for measuring delocalization in light-harvesting complexes. Direct relations between inverse participation ratios (IPRs) and entanglement measures are derived. The B850 ring from the LH2 complex in Rhodopseudomonas acidophila is studied. By analysing electronic energy transfer dynamics in the B850 ring using different metrics for quantifying excitonic delocalization, we conclude that measures of entanglement are far more robust (in terms of time scale, temperature and level of decoherence) than IPRs, and are therefore more appropriate for the purpose of studying the time evolution of coherence in a system.

Photosynthetic units perform energy transfer remarkably well under a diverse range of demanding conditions. However, the mechanism of energy transfer, from excitation to conversion, is still not fully understood. Of particular interest is the possible role that coherence plays in this process. In this perspective, we overview photosynthetic light harvesting and discuss consequences of excitons for energy transfer and how delocalization can be assessed. We focus on challenges such as decoherence and nuclear-coordinate dependent delocalization. These approaches complement conventional spectroscopy and delocalization measurement techniques. New broadband transient absorption data may help uncover the difference between electronic and vibrational coherences present in two-dimensional electronic spectroscopy data. We describe how multipartite entanglement from quantum information theory allows us to formulate measures that elucidate the delocalization length of excitation and the details of that delocalization even from highly averaged information such as the density matrix.

SummaryThe need for new methods to deal with big data is a common theme in most scientific fields, although its definition tends to vary with the context. Statistical ideas are an essential part of this, and as a partial response, a thematic program on statistical inference, learning and models in big data was held in 2015 in Canada, under the general direction of the Canadian Statistical Sciences Institute, with major funding from, and most activities located at, the Fields Institute for Research in Mathematical Sciences. This paper gives an overview of the topics covered, describing challenges and strategies that seem common to many different areas of application and including some examples of applications to make these challenges and strategies more concrete.

Time is an important feature in many applications involving events that occur synchronously and/or asynchronously. To effectively consume time information, recent studies have focused on designing new architectures. In this paper, we take an orthogonal but complementary approach by providing a model-agnostic vector representation for time, called Time2Vec, that can be easily imported into many existing and future architectures and improve their performances. We show on a range of models and problems that replacing the notion of time with its Time2Vec representation improves the performance of the final model.

Until recently, no analytical measure of many-body delocalization in open systems had been developed, yet such a measure enables characterization of how molecular excitons delocalize in photosynthetic light-harvesting complexes, and in turn helps us understand quantum coherent aspects of electronic energy transfer. In this paper we apply these measures to a model peripheral light-harvesting complex, LH2 from Rhodopseudomonas acidophila. We find how many chromophores collectively contribute to the "delocalization length" of an excitation within LH2 and how the coherent delocalization is distributed spatially. We also investigate to what extent this delocalization length is effective, by examining the impact of bipartite and multipartite entanglement in inter-ring energy transfer in LH2.