Eur. Phys. J. D (2015) 69: 36
https://doi.org/10.1140/epjd/e2014-50316-y

Regular Article

An alternative approach to the construction of Schur-Weyl transform

¹ Faculty of Mathematics and Natural Sciences, University of Rzeszów, Rejtana 16A, 35-959 Rzeszów, Poland
² Centre de Physique Théorique (CPHT), École Polytechnique, 91128 Palaiseau, France
³ Department of Physics, Rzeszów University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland

^a e-mail: kravets@cpht.polytechnique.fr

Received: 20 April 2014
Received in final form: 12 May 2014
Published online: 3 February 2015

Abstract

We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to the system, results in a change of degrees of freedom, uncovering the information hidden in non-local degrees of freedom. This information can be used, inter alia, to study the structure of entangled states, their classification and may be useful for construction of quantum algorithms.