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Register a new userMachine Learning Based Parameter Estimation of Gaussian Quantum States
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We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space displacement and squeezing parameter estimation, this is achieved by introducing Expectation-Maximization (EM) based algorithms, while for phase parameter estimation an empirical Bayes method is applied. The estimated prior distribution parameters along with the observed data are used for finding the optimal Bayesian estimate of the unknown displacement, squeezing and phase parameters. Our simulation results show that the proposed algorithms have estimation performance that is very close to that of Genie Aided Bayesian estimators, that assume perfect knowledge of the prior parameters. Our proposed methods can be utilized by experimentalists to find the optimum Bayesian estimate of parameters of Gaussian quantum states by using only the observed measurements without requiring any knowledge about the prior distribution parameters.
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We calculate the quantum Cramer--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian states. We apply the formula to the problems of estimating phase, purity, loss, amplitude, and squeezing. In the case of the simultaneous measurement of several parameters, we provide the full quantum Fisher information matrix. Our results unify previously known partial results, and constitute a complete solution to the problem of knowing the best possible sensitivity of measurements based on a single-mode Gaussian state.
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramer-Rao bound is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.
In almost all quantum applications, one of the key steps is to verify that the fidelity of the prepared quantum state meets the expectations. In this paper, we propose a new approach to solve this problem using machine learning techniques. Compared to other fidelity estimation methods, our method is applicable to arbitrary quantum states, the number of required measurement settings is small, and this number does not increase with the size of the system. For example, for a general five-qubit quantum state, only four measurement settings are required to predict its fidelity with $pm1%$ precision in a non-adversarial scenario. This machine learning-based approach for estimating quantum state fidelity has the potential to be widely used in the field of quantum information.
We investigate the quantum Cramer-Rao bounds on the joint multiple-parameter estimation with the Gaussian state as a probe. We derive the explicit right logarithmic derivative and symmetric logarithmic derivative operators in such a situation. We compute the corresponding quantum Fisher information matrices, and find that they can be fully expressed in terms of the mean displacement and covariance matrix of the Gaussian state. Finally, we give some examples to show the utility of our analytical results.
Artificial neural networks bridge input data into output results by approximately encoding the function that relates them. This is achieved after training the network with a collection of known inputs and results leading to an adjustment of the neuron connections and biases. In the context of quantum detection schemes, neural networks find a natural playground. In particular, in the presence of a target, a quantum sensor delivers a response, i.e., the input data, which can be subsequently processed by a neural network that outputs the target features. We demonstrate that adequately trained neural networks enable to characterize a target with minimal knowledge of the underlying physical model, in regimes where the quantum sensor presents complex responses, and under a significant shot noise due to a reduced number of measurements. We exemplify the method with a development for $^{171}$Yb$^{+}$ atomic sensors. However, our protocol is general, thus applicable to arbitrary quantum detection scenarios.
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