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Register a new userDetermining the maximum information gain and optimising experimental design in neutron reflectometry using the Fisher information
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An approach based on the Fisher information (FI) is developed to quantify the maximum information gain and optimal experimental design in neutron reflectometry experiments. In these experiments, the FI can be analytically calculated and used to provide sub-second predictions of parameter uncertainties. This approach can be used to influence real-time decisions about measurement angle, measurement time, contrast choice and other experimental conditions based on parameters of interest. The FI provides a lower bound on parameter estimation uncertainties and these are shown to decrease with the square root of measurement time, providing useful information for the planning and scheduling of experimental work. As the FI is computationally inexpensive to calculate, it can be computed repeatedly during the course of an experiment, saving costly beam time by signalling that sufficient data has been obtained; or saving experimental datasets by signalling that an experiment needs to continue. The approachs predictions are validated through the introduction of an experiment simulation framework that incorporates instrument-specific incident flux profiles, and through the investigation of measuring the structural properties of a phospholipid bilayer.
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Using the Fisher information (FI), the design of neutron reflectometry experiments can be optimised, leading to greater confidence in parameters of interest and better use of experimental time [Durant, Wilkins, Butler, & Cooper (2021). J. Appl. Cryst. 54, 1100-1110]. In this work, the FI is utilised in optimising the design of a wide range of reflectometry experiments. Two lipid bilayer systems are investigated to determine the optimal choice of measurement angles and liquid contrasts, in addition to the ratio of the total counting time that should be spent measuring each condition. The reduction in parameter uncertainties with the addition of underlayers to these systems is then quantified, using the FI, and validated through the use of experiment simulation and Bayesian sampling methods. For a one-shot measurement of a degrading lipid monolayer, it is shown that the common practice of measuring null-reflecting water is indeed optimal, but that the optimal measurement angle is dependent on the deuteration state of the monolayer. Finally, the framework is used to demonstrate the feasibility of measuring magnetic signals as small as $0.01mu_{B}/text{atom}$ in layers only $20r{A}$ thick, given the appropriate experimental design, and that time to reach a given level of confidence in the small magnetic moment is quantifiable.
The subjects of the paper are the likelihood method (LM) and the expected Fisher information (FI) considered from the point od view of the construction of the physical models which originate in the statistical description of phenomena. The master equation case and structural information principle are derived. Then, the phenomenological description of the information transfer is presented. The extreme physical information (EPI) method is reviewed. As if marginal, the statistical interpretation of the amplitude of the system is given. The formalism developed in this paper would be also applied in quantum information processing and quantum game theory.
For a known weak signal in additive white noise, the asymptotic performance of a locally optimum processor (LOP) is shown to be given by the Fisher information (FI) of a standardized even probability density function (PDF) of noise in three cases: (i) the maximum signal-to-noise ratio (SNR) gain for a periodic signal; (ii) the optimal asymptotic relative efficiency (ARE) for signal detection; (iii) the best cross-correlation gain (CG) for signal transmission. The minimal FI is unity, corresponding to a Gaussian PDF, whereas the FI is certainly larger than unity for any non-Gaussian PDFs. In the sense of a realizable LOP, it is found that the dichotomous noise PDF possesses an infinite FI for known weak signals perfectly processed by the corresponding LOP. The significance of FI lies in that it provides a upper bound for the performance of locally optimum processing.
In this era of Big Data, proficient use of data mining is the key to capture useful information from any dataset. As numerous data mining techniques make use of information theory concepts, in this paper, we discuss how Fisher information (FI) can be applied to analyze patterns in Big Data. The main advantage of FI is its ability to combine multiple variables together to inform us on the overall trends and stability of a system. It can therefore detect whether a system is losing dynamic order and stability, which may serve as a signal of an impending regime shift. In this work, we first provide a brief overview of Fisher information theory, followed by a simple step-by-step numerical example on how to compute FI. Finally, as a numerical demonstration, we calculate the evolution of FI for GDP per capita (current US Dollar) and total population of the USA from 1960 to 2013.
The quantum Fisher information (QFI) represents a fundamental concept in quantum physics. On the one hand, it quantifies the metrological potential of quantum states in quantum-parameter-estimation measurements. On the other hand, it is intrinsically related to the quantum geometry and multipartite entanglement of many-body systems. Here, we explore how the QFI can be estimated via randomized measurements, an approach which has the advantage of being applicable to both pure and mixed quantum states. In the latter case, our method gives access to the sub-quantum Fisher information, which sets a lower bound on the QFI. We experimentally validate this approach using two platforms: a nitrogen-vacancy center spin in diamond and a 4-qubit state provided by a superconducting quantum computer. We further perform a numerical study on a many-body spin system to illustrate the advantage of our randomized-measurement approach in estimating multipartite entanglement, as compared to quantum state tomography. Our results highlight the general applicability of our method to general quantum platforms, including solid-state spin systems, superconducting quantum computers and trapped ions, hence providing a versatile tool to explore the essential role of the QFI in quantum physics.
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