In this work we provide a method for approximating the separable numerical range of a matrix. We also recall the connection between restricted numerical range and entanglement of a quantum state. We show the possibility to establish state separability using computed restricted numerical range. In particular we present a method to obtain separability criteria for arbitrary system partition with use of the separable numerical range.

We present a novel quantum algorithm for the classification of images. The algorithm is constructed using principal component analysis and von Neuman quantum measurements. In order to apply the algorithm we present a new quantum representation of grayscale images.