Related papers: Parameter estimation for mixed states from a singl…
We obtain the optimal scheme for estimating unknown qubit mixed states when an arbitrary number N of identically prepared copies is available. We discuss the case of states in the whole Bloch sphere as well as the restricted situation where…
This paper is devoted to the study of the Bayesian-inference approach in the context of estimating the dipole coupling strength in matter-field interactions. In particular, we consider the simplest model of a two-level system interacting…
Given a finite number $N$ of copies of a qubit state we compute the maximum fidelity that can be attained using joint-measurement protocols for estimating its purity. We prove that in the asymptotic $N\to\infty$ limit, separable-measurement…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE)…
Careful tailoring the quantum state of probes offers the capability of investigating matter at unprecedented precisions. Rarely, however, the interaction with the sample is fully encompassed by a single parameter, and the information…
This paper deals with the state estimation of linear time-invariant systems using distributed observers with local sampled-data measurement and aperiodic communication. Each observer agent perceives partial information of the system to be…
In this paper we introduce two Bayesian estimators for learning the parameters of the Gamma distribution. The first algorithm uses a well known unnormalized conjugate prior for the Gamma shape and the second one uses a non-linear…
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…
It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. This property ensures the security of quantum key distribution. It is therefore an important task in quantum communication to design and…
We discuss the problem of estimating a general (mixed) qubit state. We give the optimal guess that can be inferred from any given set of measurements. For collective measurements and for a large number $N$ of copies, we show that the error…
We propose parameter optimization techniques for weighted ensemble sampling of Markov chains in the steady-state regime. Weighted ensemble consists of replicas of a Markov chain, each carrying a weight, that are periodically resampled…
We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most…
We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
We present two theoretical results on the computation of lambda-contractive sets for linear systems with state and input constraints. First, we show that it is possible to a priori compute a number of iterations that is sufficient to…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
We study the simultaneous estimation of multiple phases as a discretised model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each…
We characterize minimal measurement setups for validating the quantum coherence of an unknown quantum state. We show that for a $d$-level system, the optimal strategy consists of measuring $d$ orthonormal bases such that each measured basis…
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…