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Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well specified assumptions. The formalism is completely general and can be applied to a wide range of detectors
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Measurement connects the world of quantum phenomena to the world of classical events. It plays both a passive role, observing quantum systems, and an active one, preparing quantum states and controlling them. Surprisingly - in the light of the central status of measurement in quantum mechanics - there is no general recipe for designing a detector that measures a given observable. Compounding this, the characterization of existing detectors is typically based on partial calibrations or elaborate models. Thus, experimental specification (i.e. tomography) of a detector is of fundamental and practical importance. Here, we present the realization of quantum detector tomography: we identify the optimal positive-operator-valued measure describing the detector, with no ancillary assumptions. This result completes the triad, state, process, and detector tomography, required to fully specify an experiment. We characterize an avalanche photodiode and a photon number resolving detector capable of detecting up to eight photons. This creates a new set of tools for accurately detecting and preparing non-classical light.
Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.
In this document a review of the authors method of Fourier disentangling of spectra of binary and multiple stars is presented for the purpose of the summer school organized at Ondrejov observatory in September 2008. Related methods are also discussed and some practical hints for the use of the authors code KOREL and related auxiliary codes with examples are given.
In most fields, computational models and data analysis have become a significant part of how research is performed, in addition to the more traditional theory and experiment. Mathematics is no exception to this trend. While the system of publication and credit for theory and experiment (journals and books, often monographs) has developed and has become an expected part of the culture, how research is shared and how candidates for hiring, promotion are evaluated, software (and data) do not have the same history. A group working as part of the FORCE11 community developed a set of principles for software citation that fit software into the journal citation system, allow software to be published and then cited, and there are now over 50,000 DOIs that have been issued for software. However, some challenges remain, including: promoting the idea of software citation to developers and users; collaborating with publishers to ensure that systems collect and retain required metadata; ensuring that the rest of the scholarly infrastructure, particularly indexing sites, include software; working with communities so that software efforts count and understanding how best to cite software that has not been published.
There is an ongoing debate in computer science how algorithms should best be studied. Some scholars have argued that experimental evaluations should be conducted, others emphasize the benefits of formal analysis. We believe that this debate less of a question of either-or, because both views can be integrated into an overarching framework. It is the ambition of this paper to develop such a framework of algorithm engineering with a theoretical foundation in the philosophy of science. We take the empirical nature of algorithm engineering as a starting point. Our theoretical framework builds on three areas discussed in the philosophy of science: ontology, epistemology and methodology. In essence, ontology describes algorithm engineering as being concerned with algorithmic problems, algorithmic tasks, algorithm designs and algorithm implementations. Epistemology describes the body of knowledge of algorithm engineering as a collection of prescriptive and descriptive knowledge, residing in World 3 of Poppers Three Worlds model. Methodology refers to the steps how we can systematically enhance our knowledge of specific algorithms. In this context, we identified seven validity concerns and discuss how researchers can respond to falsification. Our framework has important implications for researching algorithms in various areas of computer science.
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