Separability and entanglement of spin $1$ particle

TL;DR

This paper explores the concepts of separability and entanglement for spin 1 particles, including qutrit states, defining measures like negativity and concurrence, and deriving new entropic inequalities.

Contribution

It introduces a framework for analyzing entanglement in spin 1 particles and qutrits, including explicit calculations and new entropic inequalities.

Findings

Maximum entanglement occurs at maximum off-diagonal density matrix elements.

Negativity and concurrence are explicitly calculated for qutrit states.

New entropic inequalities for qutrit density matrices are derived.

Abstract

We define the separability and entanglement notion for particle with spin $s=1$. We consider two cases. In the first the particle is composed of two fermions with $s_1=1/2$ and $s_2=1/2$. In the second case the state is the qutrit state which is not composed system. The notion of negativity and concurrence is defined for the qutrit state. The concurrence and negativity of entangled and separable qutrit states determined by the parameters of the density matrix are explicitly calculated. The maximum entanglement of the qutrit state is observed for maximum values of non diagonal matrix elements of the density matrix. New entropic inequalities for the density matrix of the qutrit state are obtained.