Related papers: Information and Statistical Efficiency When Quanti…
Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is…
Randomized benchmarking and variants thereof, which we collectively call RB+, are widely used to characterize the performance of quantum computers because they are simple, scalable, and robust to state-preparation and measurement errors.…
We study an industrial computer code related to nuclear safety. A major topic of interest is to assess the uncertainties tainting the results of a computer simulation. In this work we gain robustness on the quantification of a risk…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
We propose a derivation of the full counting statistics of electronic current based on a positive-operator-valued measure. Our approach justifies the Levitov-Lesovik formula in the long-time limit, but can be generalized to the detection of…
The quantum measurement process by a single-electron transistor or a quantum point contact coupled to a quantum bit is studied. We find a unified description of the statistics of the monitored quantity, the current, in the regime of strong…
The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
Phase estimation is known to be a robust method for single-qubit gate calibration in quantum computers, while Bayesian estimation is widely used in devising optimal methods for learning in quantum systems. We present Bayesian phase…
The log-likelihood of a generative model often involves both positive and negative terms. For a temporal multivariate point process, the negative term sums over all the possible event types at each time and also integrates over all the…
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 statistical model is said to be un-normalised when its likelihood function involves an intractable normalising constant. Two popular methods for parameter inference for these models are MC-MLE (Monte Carlo maximum likelihood estimation),…
Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS…
Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra…
This paper studies fixed-rate randomized vector quantization under the constraint that the quantizer's output has a given fixed probability distribution. A general representation of randomized quantizers that includes the common models in…
Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources…
This paper considers distributed average consensus using finite-bit bounded quantizer with possibly unbounded data. Under the framework of the alternating direction method of multipliers (ADMM), we develop distributed averaging algorithms…
We present a general problem formulation for optimal parameter estimation based on quantized observations, with application to antenna array communication and processing (channel estimation, time-of-arrival (TOA) and direction-of-arrival…
Quantum simulation is a central application of near-term quantum devices, pursued in both analog and digital architectures. A key challenge for both paradigms is the effect of imperfections and noise on predictive power. In this work, we…
Cram\'er type moderate deviation theorems quantify the accuracy of the relative error of the normal approximation and provide theoretical justifications for many commonly used methods in statistics. In this paper, we develop a new…