Related papers: James-Stein Estimation in Quantum Gaussian Sensing
An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is…
Randomized controlled trials (RCTs) are often underpowered to detect treatment heterogeneity in subgroups defined by cross-classifications of multiple covariates, due to sparse sample sizes in some strata. External RCT data can help, but…
Given $n$ i.i.d. samples from an unknown discrete distribution over an unknown set, the unseen species problem is to predict how many new outcomes would be observed in $m$ additional samples. For small $m$ we show that the Good-Toulmin…
Probabilistic metrology attempts to improve parameter estimation by occasionally reporting an excellent estimate and the rest of the time either guessing or doing nothing at all. Here we show that probabilistic metrology can never improve…
Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…
We study quantum steering experiments without assuming that the trusted party can perfectly control their measurement device. Instead, we introduce a scenario in which these measurements are subject to small imprecision. We show that small…
We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we…
Predicting the outcomes of quantum measurements is a cornerstone of quantum information theory and a key resource for quantum technologies. Here, we introduce a comprehensive framework for quantifying the predictability of measurements on a…
Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum…
We consider the system identification problem of estimating a dynamical parameter of a Markovian quantum open system (the atom maser), by performing continuous time measurements in the system's output (outgoing atoms). Two estimation…
Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the…
Quantum phase estimation (QPE) is one of the most important subroutines in quantum computing. In general applications, current QPE algorithms either suffer an exponential time overload or require a set of - notoriously quite fragile - GHZ…
In the context of Independent Component Analysis (ICA), noisy mixtures pose a dilemma regarding the desired objective. On one hand, a "maximally separating" solution, providing the minimal attainable Interference-to-Source-Ratio (ISR),…
Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory.…
Quantum instruments describe both the classical outcome and the updated state associated with a quantum measurement. We ask whether these processes can be simulated using only a natural subset of resources, namely projective measurements on…
The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for…
Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
We analyze the problem of estimating a signal from multiple measurements on a $\mbox{group action channel}$ that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel…
High precision measurements are essential to solve major scientific and technological challenges, from gravitational wave detection to healthcare diagnostics. Quantum sensing delivers greater precision, but an in-depth optimisation of…