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Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…
We examine the statistics of current fluctuations in a junction with a quantum dot described by Kondo Hamiltonian. With the help of Keldysh technique we calculate shot noise as a function of applied voltage at zero temperature using the…
It is important to know noise levels of boson sampling in order to cautiously demonstrate the quantum computational advantage or realize certain tasks. Based on those statistical benchmark methods such as the correlators and clouds, which…
In this thesis we consider primarily the dynamics of quantum systems subjected to continuous observation. In the Schr\"{o}dinger picture the evolution of a continuously monitored quantum system, referred to as a `quantum trajectory', may be…
We present a quantum calculation based on scattering theory of the frequency dependent noise of current in an interacting chaotic cavity. We include interactions of the electron system via long range Coulomb forces between the conductor and…
Monitoring a quantum observable continuously in time produces a stochastic measurement record that noisily tracks the observable. For a classical process such noise may be reduced to recover an average signal by minimizing the mean squared…
Today's mechanical sensors are capable of detecting extremely weak perturbations while operating near the standard quantum limit. However, further improvements can be made in both sensitivity and bandwidth when we reduce the noise…
Detection of weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. We consider a quantum system initialized in a pure state and whose evolution is governed by a…
In this brief paper, we present a simple approach to estimate the variance of measurement noise with time-varying 1-D signals. The proposed approach exploits the relationship between the noise variance and the variance of the prediction…
Analysis of experimental data must sometimes deal with abrupt changes in the distribution of measured values. Setting upper limits on signals usually involves a veto procedure that excludes data not described by an assumed statistical…
A significant problem for current quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model often appropriately describes average noise for large circuits involving many qubits and gates. We…
This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…
We consider the electromagnetic field generated by a coherent conductor in which electron transport is described quantum mechanically. We obtain an input-output relation linking the quantum current in the conductor to the measured…
We consider functional data which are measured on a discrete set of observation points. Often such data are measured with additional noise. We explore in this paper the factor structure underlying this type of data. We show that the latent…
Time-dependent driving influences the quantum and thermodynamic fluctuations of a system, changing the familiar physical picture of electronic noise which is an important source of information the about microscopic mechanism of quantum…
Systems near to quantum critical points show universal scaling in their response functions. We consider whether this scaling is reflected in their fluctuations; namely in current-noise. Naive scaling predicts low-temperature Johnson noise…
Low-frequency noise presents a serious source of decoherence in solid-state qubits. When combined with a continuous weak measurement of the eigenstates, the low-frequency noise induces a second-order relaxation between the qubit states.…
This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…
In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum…
We propose a setup for a quantitative test of the quantum fluctuation theorem. It consists of a quantum conductor, driven by an external voltage source, and a classical inductor-capacitor circuit. The work done on the system by the voltage…