Related papers: Optimal error regions for quantum state estimation

We construct an optimal quantum universal variable-length code that achieves the admissible minimum rate, i.e., our code is used for any probability distribution of quantum states. Its probability of exceeding the admissible minimum rate…

We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design…

The relative error of cloning of quantum states with arbitrary prior probabilities is considered. It is assumed that the ancilla may contain some a priori information about the input state to be cloned. The lower bound on the relative error…

Quantum bits, or qubits, are the fundamental building blocks of present quantum computers. Hence, it is important to be able to characterize the state of a qubit as accurately as possible. By evaluating the qubit characterization problem…

We investigate a state discrimination problem which interpolates minimum-error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence…

In this work, we consider optimal state discrimination for a quantum system that interacts with an environment, i.e., states evolve under a quantum channel. We show the conditions on a quantum channel and an ensemble of states such that a…

Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…

The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…

Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…

Experimental characterizations of a quantum system involve the measurement of expectation values of observables for a preparable state |psi> of the quantum system. Such expectation values can be measured by repeatedly preparing |psi> and…

In this paper we introduce a method, which is used for set separation based on quantum computation. In case of no a-priori knowledge about the source signal distribution, it is a challenging task to find an optimal decision rule which could…

Measuring the closest distance between two states is an alternative and significant approach in the resource quantification, which is the core task in the resource theory. Quite limited progress has been made for this approach even in…

Designing experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. The local optimality approach is to study the regions in parameter space where a given design is optimal. In many…

We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it allows to derive the ultimate bounds of the achievable precision. We show a relation between the statistical distance…

The root estimator of quantum states based on the expansion of the psi function in terms of system eigenfunctions followed by estimating the expansion coefficients by the maximum likelihood method is considered. In order to provide…

We describe an optimized, self-correcting procedure for the Bayesian inference of pure quantum states. By analyzing the history of measurement outcomes at each step, the procedure returns the most likely pure state, as well as the optimal…

The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation…

We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…