Towards properly controlled analytical measurement methods

It is of great practical importance to develop simple methods for the automatic detection ofthe controlled state of the analytical method being applied. The key point is to find quantities that greatly affect the quality of the analytical results and that can be easily estimated during the measurement process from the measured data. The signal-to-noise ratio has proved to be such a quantity in gas chromatographic methods. The statistical properties of the estimation of the signal-to-noise ratio from gas chromatographic data have been investigated. The suggested practical method for estimating the signal-to-noise ratio proved to be biased from a mathematical statistical point of view, but the bias is usually not greater than 10%. It has been shown by practical examples that the signal-to-noise ratio affects the quality of the analytical results and it is easy to estimate its value from practical data

Investigation of the steady state measurement process

Based on the role of steady state concept in the model of analytical chemical measurement and deduction, the definition of ‘practically sleady slate’ (PSS) has been inlroduced. The defnition does not require the process to be in steady state in a strictly mathematical sense. In order to fulfil the requiremenls of ‘practically steady state’ the random error and the syslematic error must vary within a suitable limit, and the expected fgure for the measured value must be within a specified range

State tomography for two qubits using reduced densities

The optimal state determination (or tomography) is studied for a composite system of two qubits when measurements can be performed on one of the qubits and interactions of the two qubits can be implemented. The goal is to minimize the number of interactions to be used. The algebraic method applied in the paper leads to an extension of the concept of mutually unbiased measurements.Comment: 8 pages LATE

Towards properly controlled analytical measurement methods

It is o f great practical importance to develop simple methods for the automatic detection of the controlled state of the analytical method being applied. The key point is to find quantities that greatly affect the quality of the analytical results and that can be easily estimated during the measurement process from the measured data. The signal-to-noise ratio has proved to be such a quantity in gas chromatographic methods. The statistical properties of the estimation of the signal-to-noise ratio from gas chromatographic data have been investigated. The suggested practical method for estimating the signal-to-noise ratio proved to be biased from a mathematical statistical point of view, but the bias is usually not greater than 10%. It has been shown by practical examples that the signal-to-noise ratio affects the quality of the analytical results and it is easy to estimate its value from practical data

Point Estimation of States of Finite Quantum Systems

The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the properties of the estimation procedure depend very much on the invertibility of the true state. In particular, in case of a pure state the estimation is less efficient. Moreover, several estimation schemes are compared for the unknown state of a qubit when one copy is measured at a time. It is shown that the average mean quadratic error matrix is the smallest if the applied observables are complementary. The results are illustrated by computer simulations.Comment: 16 pages, 5 figure