This paper contains a characterization of certain aspects of bipartite quantum entanglement. We discuss relationship between entropy and entanglement, as well as qualitative and quantitative aspects of entanglement. Qualitative characterization of entanglement concerns the criteria: reduction criterion, positive partial transpose, positive maps, entanglement witness and majorization criterion. Measures of entanglement have been discussed as the quantitative aspects of entanglement.
PL
W artykule zostały poruszone podstawowe aspekty splątania kwantowego. Przytoczone zostały definicje splątania dla stanów czystych oraz mieszanych. Następnie opisano pojęcie entropii von Neumanna oraz jej związek ze splątaniem stanów kwantowych. Kolejne sekcje zawierają opis kryteriów separowalności. Ostatnia sekcja zawiera aksjomaty miar splątania, a także najważniejsze miary splątania.
This paper describes how to calculate the number of algebraic operations necessary to implement block matrix inversion that occurs, among others, in mathematical models of modern positioning systems of mass storage devices. The inversion method of block matrices is presented as well. The presented form of general formulas describing the calculation complexity of inverted form of block matrix were prepared for three different cases of division into internal blocks. The obtained results are compared with a standard Gaussian method and the “inv” method used in Matlab. The proposed method for matrix inversion is much more effective in comparison in standard Matlab matrix inversion “inv” function (almost two times faster) and is much less numerically complex than standard Gauss method.