Related papers: Optimal Correlation Estimators for Quantized Signa…
Signal extraction out of background noise is a common challenge in high precision physics experiments, where the measurement output is often a continuous data stream. To improve the signal to noise ratio of the detection, witness sensors…
Ultra-cold atoms in optical lattices provide one of the most promising platforms for analog quantum simulations of complex quantum many-body systems. Large-size systems can now routinely be reached and are already used to probe a large…
We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator.…
A simple derivation of the optimal state estimation of a quantum bit was obtained by using the no-signaling principle. In particular, the no-signaling principle determines a unique form of the guessing probability independently of figures…
We study estimation of an $s$-sparse signal in the $p$-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely the rate scales with respect to…
Noise radars can be understood in terms of a correlation coefficient which characterizes their detection performance. Although most results in the literature are stated in terms of the signal-to-noise ratio (SNR), we show that it is…
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this…
We consider the classical problem of estimating the covariance matrix of a subgaussian distribution from i.i.d. samples in the novel context of coarse quantization, i.e., instead of having full knowledge of the samples, they are quantized…
In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…
This paper analyzes the impact of spatially correlated additive noise on the minimum mean-square error (MMSE) estimation of multiple-input multiple-output (MIMO) channels from one-bit quantized observations. Although additive noise can be…
We study the matrix denoising problem of estimating the singular vectors of a rank-$1$ signal corrupted by noise with both column and row correlations. Existing works are either unable to pinpoint the exact asymptotic estimation error or,…
We consider linear time-varying channels with additive white Gaussian noise. For a large class of such channels we derive rigorous estimates of the eigenvalues of the correlation matrix of the effective channel in terms of the sampled…
We present methods and results of shot-by-shot correlation of noisy measurements to extract entangled state and process tomography in a superconducting qubit architecture. We show that averaging continuous values, rather than counting…
Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…
Constructive theory of characterization test is considered. The theory is applicable to a nano devices characterization: current-voltage, Auger current dependence. Generally small response of device under test on an applied stimulus is…
The problem of detecting correlations from samples of a high-dimensional Gaussian vector has recently received a lot of attention. In most existing work, detection procedures are provided with a full sample. However, following common wisdom…
We introduce a novel approach to estimation problems in settings with missing data. Our proposal -- the Correlation-Assisted Missing data (CAM) estimator -- works by exploiting the relationship between the observations with missing features…
This paper is concerned with an optimal investment problem under correlated noises in the financial market, and the expected utility functional is hyperbolic absolute risk aversion (HARA) with the exponent $\gamma\neq0$. The problem can be…
The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always…
We develop strategies for enhancing the signal/noise ratio for stochastically sampled correlation functions. The techniques are general and offer a wide range of applicability. We demonstrate the potential of the approach with a generic…