# Separability and entanglement in the Hilbert space reference frames related through the generic unitary transform for four level system

## TL;DR

This paper explores how unitary transformations of the reference frame in a four-level quantum system influence entanglement, analyzing various states and their quantum correlations through geometrical and quantitative measures.

## Contribution

It introduces a detailed analysis of entanglement generation via Hilbert space rotations for four-level systems, including pure, X, and Werner states, with explicit characterizations.

## Key findings

- Unitary transformations can generate entanglement from initially separable states.
- Entanglement measures vary as functions of the unitary rotation parameters.
- Geometrical interpretation of reference frame rotations provides insight into entanglement dynamics.

## Abstract

Quantum correlations in the state of four-level atom are investigated by using generic unitary transforms of the classical (diagonal) density matrix. Partial cases of pure state, $X$-state, Werner state are studied in details. The geometrical meaning of unitary Hilbert reference-frame rotations generating entanglement in the initially separable state is discussed. Characteristics of the entanglement in terms of concurrence, entropy and negativity are obtained as functions of the unitary matrix rotating the reference frame.