Related papers: Scalar Quantization with Random Thresholds
We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an…
We study the scaling of the convergence of several statistical properties of a recently introduced random unitary circuit ensemble towards their limits given by the circular unitary ensemble (CUE). Our study includes the full distribution…
We study the quantum summation (QS) algorithm of Brassard, Hoyer, Mosca and Tapp, that approximates the arithmetic mean of a Boolean function defined on N elements. We improve error bounds presented in [1] in the worst-probabilistic…
We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte…
Multilevel Splitting methods, also called Sequential Monte-Carlo or \emph{Subset Simulation}, are widely used methods for estimating extreme probabilities of the form $P[S(\mathbf{U}) > q]$ where $S$ is a deterministic real-valued function…
Predictive design and optimization methods for controlled quantum systems depend on the accuracy of the system model. Any distortion of the input fields in an experimental platform alters the model accuracy and eventually disturbs the…
We derive fundamental lower bounds on the performance of optical metrology and communication systems in a Bayesian framework. The derivation uses classical rate-distortion theory in conjunction with bounds on the capacity to transmit…
Constant gain least-mean-squares (LMS) algorithms have a wide range of applications in trajectory tracking problems, but the formal convergence of LMS in mean square is not yet fully established. This work provides an upper bound on the…
In this paper we show how different sources of random numbers influence the outcomes of Monte Carlo simulations. We compare industry-standard pseudo-random number generators (PRNGs) to a quantum random number generator (QRNG) and show,…
We consider the problem of transmission of a sequence of real data produced by a Nyquist sampled band-limited analog source over a band-limited analog channel, which introduces an additive white Gaussian noise. An analog coding scheme is…
This paper is concerned with scalar quantization of transform coefficients in an audio codec. The generalized Gaussian distribution (GGD) is used as an approximation of one-dimensional probability density function for transform coefficients…
We introduce a general framework for end-to-end optimization of the rate--distortion performance of nonlinear transform codes assuming scalar quantization. The framework can be used to optimize any differentiable pair of analysis and…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…
We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is…
Consider a generalized multiterminal source coding system, where $\ell\choose m$ encoders, each observing a distinct size-$m$ subset of $\ell$ ($\ell\geq 2$) zero-mean unit-variance symmetrically correlated Gaussian sources with correlation…
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…