Quantifying entanglement of two relativistic particles using optimal entanglement witness

In a recent paper, it was shown that the projections of a relativistic spin operator (RSO) massive spin-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\frac{1}{2}}$$\end{document} particle on a world-vector which can be in timelike or null tetrad direction are proportional to the helicity or Bargman-Wigner (BW) qubit, respectively. Here we consider Lorentz transformations of two-particle states, which have been constructed both in helicity basis. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) for each particle. Consequently, in 2D momentum subspace we describe the structure of one particle in terms of the four-qubit system. We present a new approach to quantification of relativistic entanglement based on entanglement witness (EW), which is obtained by a new method of convex optimization. In addition, Lorentz invariance of entanglement using BW qubit is also studied.