Related papers: Optimal measurements in quantum mechanics
We study various optimality criteria for quantum observables. Observables are represented as covariant positive operator valued measures and we consider the case when the symmetry group is compact. Phase observables are examined as an…
Joint or simultaneous measurements of non-commuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for defining what an "optimal" joint measurement is, with…
Knowledge of optimal quantum measurements is important for a wide range of situations, including quantum communication and quantum metrology. Quantum measurements are usually optimised with an ideal experimental realisation in mind. Real…
Various forms of optimality for quantum observables described as normalized positive operator valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity…
Optimal and finite positive operator valued measurements on a finite number $N$ of identically prepared systems have been presented recently. With physical realization in mind we propose here optimal and minimal generalized quantum…
We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating…
As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and…
Basic quantum information measures involved in the information analysis of quantum systems are considered. It is shown that the main quantum information measurement methods depend on whether the corresponding quantum events are compatible…
We derive the class of covariant measurements which are optimal according to the maximum likelihood criterion. The optimization problem is fully resolved in the case of pure input states, under the physically meaningful hypotheses of…
We consider the problem of estimating the ensemble average of an observable on an ensemble of equally prepared identical quantum systems. We show that, among all kinds of measurements performed jointly on the copies, the optimal unbiased…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.
We point out a general framework that encompasses most cases in which quantum effects enable an increase in precision when estimating a parameter (quantum metrology). The typical quantum precision-enhancement is of the order of the square…
We study quantum learning algorithms for quantum measurements. The optimal learning algorithm is derived for arbitrary von Neumann measurements in the case of training with one or two examples. The analysis of the case of three examples…
We discuss symmetric quantum measurements and the associated covariant observables modelled, respectively, as instruments and positive-operator-valued measures. The emphasis of this work are the optimality properties of the measurements,…
Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a…
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…
Any observable with finite eigenvalue spectrum can be measured using a multiport apparatus realizing an appropriate unitary transformation and an array of detector instruments, where each detector operates as an indicator of one possible…