An alternative approach to the construction of Schur-Weyl transform

TL;DR

This paper introduces a new method for constructing a unitary matrix that performs generalized rotations on multi-partite quantum systems, revealing hidden information and aiding in entanglement analysis and quantum algorithm development.

Contribution

It presents an alternative approach to the Schur-Weyl transform for creating unitary matrices that change system degrees of freedom in quantum systems.

Findings

Enables analysis of entangled states

Facilitates classification of quantum states

Potential applications in quantum algorithms

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.